Dynamic modeling and optimal control method of dual information collaborative diffusion process in social networks

Abstract

A dynamic modeling method for the collaborative diffusion process of dual information in social networks is characterized by establishing a dual information collaborative diffusion dynamics model based on ordinary differential equations based on two information diffusion pathways of social contact and random contact of users in social networks to accurately characterize the collaborative diffusion process of dual information related to the same event in social networks. This method can provide a certain theoretical basis and technical support for the efficient and controllable dissemination of information in social networks, and provide a certain reference for the prediction of information dissemination trends in social networks and related application scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field of social network, and specifically relates to a dynamic modeling and optimal control method for a dual information collaborative diffusion process in a social network. Background Art

[0002] With the rapid development of instant messaging technology and the rapid popularization of smart terminal devices, social networks have gradually emerged and become the main platform for people to spread and share information. Social networks can provide a variety of information services to the public. The advantages of simplicity, speed and distance make social networks penetrate into all areas of people's work and life. At present, they have become a frontier research direction in the field of electronic information and new networks. In recent years, social networks that integrate Internet of Things technology and big data technology have shown broad application prospects in application fields such as news dissemination, mobile communications, online education, smart homes and e-commerce, attracting widespread attention from industry and academia.

[0003] Social networks are highly open networks. In social networks, each user is the subject of sending and receiving information, and users can independently select and forward various information of interest. In a huge network, information can spread quickly to every corner of the world. In this case, if bad information, such as rumors and false news, spreads in social networks, it may cause certain misleading and losses to network users; if authoritative news and false news spread in social networks at the same time, due to the subjectivity of user judgment and the autonomy of forwarding messages,

[0004] False information may hinder the spread of authoritative news. In particular, when a hot event breaks out, multiple messages about the event are intertwined and spread in social networks at the same time, making it impossible to accurately grasp the spread trend and scope of the event, and thus unable to effectively guide public opinion. Therefore, how to model the diffusion process of information and predict its diffusion trend, and then effectively regulate it, has become an urgent problem to be solved in the basic research of social network applications.

[0005] Relevant research work in recent years shows that the main modeling methods for the information diffusion process in social networks are the micro-based information diffusion cascade modeling method and the macro-based information diffusion dynamics modeling method. Existing research work mainly focuses on the diffusion process modeling of single information and semantically positive and negative dual information in social networks, while research on the modeling of the collaborative diffusion process of dual information of the same event is still in its infancy. The main methods for regulating the information diffusion process in social networks are the information diffusion source blocking method and the information diffusion process regulation method. Existing research work related to information diffusion regulation is still focused on single information diffusion regulation and competitive information diffusion regulation. There is no literature report on the research work on the regulation of the collaborative diffusion process of dual information of the same event. Summary of the invention

[0006] In view of this, the present disclosure provides a dynamic modeling method for the collaborative diffusion process of dual information in social networks, which is characterized by establishing a dual information collaborative diffusion dynamics model based on ordinary differential equations based on two information diffusion pathways of social contact and random contact of users in social networks to accurately characterize the collaborative diffusion process of dual information related to the same event in social networks.

[0007] Through the above technical solution, the collaborative diffusion process of two pieces of information related to the same event in social networks is effectively modeled, and on this basis, the overall diffusion trend of event information is predicted, and the optimal control method for the collaborative diffusion process of two pieces of information is further proposed. The main contributions of this disclosure include the following four aspects:

[0008] 1) Focusing on the modeling and optimal regulation of the collaborative diffusion process of dual information related to the same event in social networks, a dual information collaborative diffusion dynamics model and optimal regulation method were proposed for the first time.

[0009] 2) Considering the two information diffusion pathways of social contact and random contact among users in social networks, a dynamic model based on ordinary differential equations is established to accurately characterize the dual information collaborative diffusion process.

[0010] 3) The evolution law of the coordinated diffusion of dual information is analyzed theoretically, and the necessary conditions for whether information can explode in the network or disappear over time are derived, and the trend of the coordinated diffusion of dual information is further predicted.

[0011] 4) For different users, two types of information diffusion control strategies are proposed, with the overall goal of maximizing information diffusion and minimizing control costs. The optimal control theory is used to establish the corresponding optimal control system and solve the optimal dynamic distribution of the control strategy over time. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 is a schematic diagram of the relationship between user information status and information status transfer in one embodiment of the present disclosure;

[0013] Figure 2 is a schematic diagram of a dual information collaborative diffusion control model in one embodiment of the present disclosure;

[0014] Figure 3 is a diagram of experimental results of Case 1 in one embodiment of the present disclosure;

[0015] Figure 4 This is a diagram of experimental results of Case 2 of an embodiment of the present disclosure;

[0016] Figure 5 is a diagram of parameter sensitivity analysis results in one embodiment of the present disclosure;

[0017] Figure 6 is a diagram of parameter PRCC analysis results in one embodiment of the present disclosure;

[0018] Figure 7 is a diagram of experimental results of case 3 in one embodiment of the present disclosure;

[0019] Figure 8 is a diagram of experimental results of case 4 in one embodiment of the present disclosure;

[0020] Fig. 9 is a diagram of experimental results of Case 5 in one embodiment of the present disclosure;

[0021] Fig.10 is a graph of experimental results of Case 6 in one embodiment of the present disclosure;

[0022] Fig.11 is a diagram of experimental results of Case 7 in one embodiment of the present disclosure;

[0023] Fig.12 is a diagram of experimental results of Case 8 in one embodiment of the present disclosure;

[0024] Fig.13 It is a diagram of the system utility analysis results in Cases 1-8 in one embodiment of the present disclosure. DETAILED DESCRIPTION

[0025] The following will refer to the attached Figures 1 to 13 Specific embodiments of the present disclosure are described in detail.

[0026] In one embodiment, a dynamic modeling method for the collaborative diffusion process of dual information in a social network is disclosed, which is characterized in that a dual information collaborative diffusion dynamics model based on ordinary differential equations is established based on two information diffusion pathways, namely social contact and random contact of users in the social network, to accurately characterize the collaborative diffusion process of dual information related to the same event in the social network.

[0027] As far as this embodiment is concerned, the method can provide a certain theoretical basis and technical support for the efficient and controllable dissemination of information in social networks, and provide a certain reference for the prediction of information dissemination trends in social networks and related application scenarios.

[0028] In another embodiment, the social contact means that each user in the user set can use the directed edges between the user and his / her neighbors in the social network to achieve directed diffusion of information.

[0029] In another embodiment, the random contact means that each user in the user set will be connected to some random information sources to achieve information diffusion.

[0030] In this embodiment, the random information source is, for example, the user is exposed to offline announcements and promotions, and obtains information offline through word of mouth.

[0031] In another embodiment, the modeling method of the dual information cooperative diffusion dynamics model specifically includes the following steps:

[0032] S100: Given a social network G = {V, E}, where V represents a set of users and E represents a set of directed edges;

[0033] S200: When the information Mes1 and Mes2 related to the same event spread in the social network, let<S1,S2> (t),<I1,S2> (t),<S1,I2> (t), <r>(t) respectively represent the<S1,S2> ,<I1,S2> ,<S1,I2> , <r>The proportion of users in<S1,S2> It means that the user has not received the information Mes1 and Mes2 at present, but may receive them in the future;<I1,S2> It means that the user has currently received information Mes1, but has not received information Mes2, and is likely to spread information Mes1 to other users in the social network;<S1,I2> : Indicates that the user has currently received information Mes2, but has not received information Mes1. Similarly, the user may spread the received information Mes2 to other users in the social network; It means that the user has currently received both information Mes1 and Mes2, and the user receives information Mes1 earlier than information Mes2. In addition, the user may spread information Mes1 and Mes2 to other users in the social network; It means that the user has currently received both information Mes1 and Mes2, and the information Mes2 is received earlier than the information Mes1, and the user is likely to spread the information Mes1 and Mes2 to other users in the social network; <r>The user currently loses interest in information Mes1 and Mes2, is unwilling to receive them, and does not participate in their diffusion process;

[0034] S300: The dual information cooperative diffusion dynamics model of Mes1 and Mes2 is established as follows:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] The initial value of the model is:

[0042]

[0043] The constraints of the model are:

[0044]

[0045] in, p1 and p2 represent the probability of a user receiving information from the social contact layer and the random contact layer, respectively. δ represents the probability of a user losing interest in information and undergoing a state transition. λ represents the probability of a user rekindling interest in information and undergoing a state transition. α represents<S1,S2> After receiving the message Mes1, the state user transfers to<I1,S2> The probability of the state, β represents<S1,S2> After receiving the message Mes2, the state user transfers to<S1,I2> The probability of the state, γ represents<I1,S2> After receiving the message Mes2, the state user transfers to The probability of the state, η represents<S1,I2> After receiving the message Mes1, the state user transfers to In this embodiment, the set of users participating in the dual information collaborative diffusion process is defined as V = {1, 2, n-1, n}, and the social network between users is G = {V, E}. E represents a set of directed edges, where e i，j ∈E represents the edge from user i to j, then |E| = m. Information can be freely diffused among all users in G. n is the number of users, n∈[2, +∞), and n is a real number. m is the number of edges between users, m∈[1, +∞), and m is a real number.

[0046] When the information Mes1 and Mes2 related to the same event are diffused in the network in coordination, we divide the information status of users participating in the information diffusion process into the following six types according to the different situations of users receiving or forwarding information: 1)<S1,S2> 2)<I1,S2> 3)<S1,I2> 4) 5) 6) <r>At any time, the users in set V belong to one of the above six information states and can switch between the above information states. Table 1 gives the attributes of users in various information states.

[0047]

[0048]

[0049] Table 1

[0050] Input of the dynamic modeling problem of dual information cooperative diffusion process: G = {V, E}, Mes1 and Mes2.

[0051] Output of the dynamic modeling problem of dual information cooperative diffusion process: about A dual information cooperative diffusion dynamics model.

[0052] Inspired by the diffusion theory based on the infectious disease model in information theory, when the information Mes1 and Mes2 related to the same event spread in the network, Figure 1 Indicates the six information states of the user and the transition relationship between the user's various information states. Figure 1 As shown in the figure, there are three main types of state transfer relationships between users:

[0053] (1) Directed edges express The information status of users is subject to the diffusible Mes k The influence of information users has transformed into Information status, x∈{α,β,γ,η} indicates that the user believes and receives the information Mes k It is worth noting that p1 and p2 are used to represent the probability that a user receives information from the social contact layer and the random contact layer, respectively.

[0054] (2) Directed edges express Users in the information state are no longer interested in the information and turn to <r>Information status, where δ represents the probability of a user's state transition due to losing interest in information.

[0055] (3) Directed edges express <r>Users in the information state have renewed their interest in information and thus become<S1,S2> Information state, similarly, λ represents the current state transition probability.

[0056] In the above nonlinear dynamic model, the evolution process of the user state ratio caused by the diffusion of Mes1 and Mes2 in the network is described according to the initial value (7) and the state equations (1)-(6), which can reflect the diffusion process of Mes1 and Mes2 in the network from a macro perspective.

[0057] In another embodiment, a method for predicting the trend of dual information collaborative diffusion based on the dual information collaborative diffusion kinetic model comprises the following steps:

[0058] S400: extracting sub-items with the ability to forward Mes1 and Mes2 from the dual information cooperative diffusion dynamics model to form the following diffusion equation:

[0059]

[0060] Where X satisfies the following matrix:

[0061]

[0062] in,

[0063]

[0064]

[0065] S500: Calculated and The derivative in the zero equilibrium state is:

[0066]

[0067] Where f1 =<S1,S2> (0)(p1+p2)α, f2=<S1,S2> (0)(p1+p2)β;

[0068] S600: Construct the following characteristic equation:

[0069]

[0070] By solving the characteristic roots of the above characteristic equation, the joint basic reproduction number of Mes1 and Mes2 cooperative diffusion can be calculated:

[0071]

[0072] Among them It indicates the influence degree of users with forwarding capability on other users in the collaborative diffusion process of Mes1 and Mes2;

[0073] S700: According to the combined basic regeneration number Determine whether the coordinated diffusion of Mes1 and Mes2 breaks out in the social network.

[0074] In this embodiment, based on the dual information collaborative diffusion dynamics model established above, the evolution law of dual information collaborative diffusion is analyzed, the necessary conditions for Mes1 and Mes2 to continue to diffuse or automatically disappear in the network are derived, and the diffusion trend of Mes1 and Mes2 is further predicted. Input of the prediction problem of dual information collaborative diffusion trend: dual information collaborative diffusion dynamics model; Output of the prediction problem of dual information collaborative diffusion trend: joint basic reproduction number corresponding to the model Joint diffusion trend of Mes1 and Mes2

[0075] When there is no diffusion of Mes1 and Mes2 information in the network, the model is in a zero equilibrium state (<S1,S2> (0), 0, 0, 0, 0, 0).

[0076] In another embodiment, the step S700 further includes:

[0077] S701: If The number of users with forwarding capabilities in the social network will gradually decrease, the coordinated diffusion of Mes1 and Mes2 will not be able to break out, and will gradually die out over time. The information will eventually disappear in the social network and reach a stable state.

[0078] S702: If The number of users with forwarding capabilities in social networks will gradually increase, and the coordinated diffusion of Mes1 and Mes2 will break out and continue to spread in social networks. The larger R0 is, the more obvious the outbreak trend will be.

[0079] For this embodiment,

[0080]

[0081] In another embodiment, a method for optimally controlling the dual information cooperative diffusion based on the dual information cooperative diffusion dynamics model comprises the following steps:

[0082] S800: Propose different information diffusion control strategies for users with different information status;

[0083] S900: Establishment of a dual information cooperative diffusion control dynamics system;

[0084] S1000: Based on optimal control theory, solve the optimal solution distribution of control strategy over time.

[0085] In this embodiment, S800 is to propose different types of strategies, and S1000 is to calculate the optimal solution distribution of these strategies over time, that is, the optimal execution amount at each time point. Propose a set of control strategies C for the diffusion of Mes1 and Mes2 i , establish the optimal control method of dual information collaborative diffusion, under the premise of control budget constraints and within a given control period [0, T], how to solve the optimal solution distribution of the control strategy so that the diffusion of Mes1 and Mes2 is maximized and the control cost is minimized, that is:

[0086]

[0087]

[0088] 0≤<S1,S2> (t)≤1,0<<I1,S2> (t)≤1,0<<S1,I2> (t)≤1,

[0089]

[0090]

[0091] in: represents the diffusion range of Mes1 and Mes2 at time t, Indicates that control measure C is implemented at time t i The control cost consumed. The first line of the above constraint indicates that the total control cost does not exceed budget B; the second and third lines are the user ratio constraints for each state, and the fourth line indicates that the sum of all state ratios is 1.

[0092] Input of the optimal control problem of dual information cooperative diffusion: dual information cooperative diffusion dynamics model, control strategy set C i and control budget B.

[0093] Output of the optimal control problem of dual information cooperative diffusion: optimal control model and distribution of optimal solutions of control strategy

[0094] For problem (P), a dual information collaborative diffusion optimal control method is proposed to maximize the diffusion of Mes1 and Mes2 without exceeding the control budget B. First, targeted information diffusion control strategies are proposed for users with different information states; then, an optimal control system for information diffusion control is established; finally, based on the optimal control theory, the optimal solution distribution of the control strategy over time is solved.

[0095] In another embodiment, the information diffusion regulation strategy includes a single information weak attraction strategy and a double information strong attraction strategy.

[0096] In this embodiment, two information diffusion control strategies with synergistic effects are designed for users in different information states, so as to further accelerate the process of dual information synergistic diffusion in the network.

[0097] Combining the above control strategies, a dual information collaborative diffusion control model is established. Figure 2 The state transfer rate equation in the model is as follows:

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] Formulas (10)-(15) constitute a dual-information cooperative diffusion control dynamic system, which still satisfies the initial value conditions in formula (7) and the constraints in formula (8). In addition, it satisfies the following control strategy boundary conditions:

[0105]

[0106] It is worth noting that when regulating the dual information collaborative diffusion process, an important constraint that must be considered is the limited control cost. In real scenarios, due to the limitations of human or physical resources, we often cannot impose control measures regardless of cost. Define the implementation of all control strategies C at time t i The fees are as follows:

[0107]

[0108] Among them, k1, k2, k3 and k4 are positive constants.

[0109] Furthermore, the diffusion influence range of Mes1 and Mes2 at time t is defined as follows:

[0110]

[0111] Among them, p and q are positive constants, which are used to represent and The diffusion range utility weight of the state user.

[0112] Furthermore, the problem (P) can be rewritten as follows:

[0113]

[0114] In view of the above problem, in order to solve the control strategy that maximizes the diffusion range of Mes1 and Mes2 and minimizes the control cost in the entire control cycle [0, T], the optimal control theory is used to solve the optimal solution to the problem.

[0115] First, the Lagrange equation for solving problem (P) is constructed as follows:

[0116]

[0117] The problem (P) can be further transformed into a solution The maximum value of . The Hamiltonian function that meets this problem is constructed as follows:

[0118]

[0119] in, λ <r>< / r> (t) is the adjoint equation, let<S1,S2> * (t),<I1,S2> * (t),<S1,I2> * (t), <r> * (t) is the optimal control strategy C of the dual information cooperative communication system * (t)∈{μ * (t),ω * (t), θ * (t), σ * (t)}. Similarly, let The optimal control strategy The corresponding adjoint equation solution. Substituting (10)-(15) and formula (20) into the above formula, we get:

[0120]

[0121] In order to facilitate description, we omit (t) in the formula variables.

[0122] The optimal solution distribution of problem (P) is solved by using the Pondriagin maximum principle, and the following conclusions are given:

[0123] Let the optimal solution that satisfies the problem (P) at time t and the corresponding system state equation solution and adjoint equation solution constitute the set There must be a A non-trivial vector of It satisfies:

[0124]

[0125]

[0126]

[0127] in,

[0128] According to the Hamiltonian function shown in the above formula (25) and formula (22), the adjoint equation of the dual information cooperative propagation control system can be obtained as follows:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] When t=T, the above formulas (26)-(31) have the following boundary conditions:

[0136]

[0137] Further, according to formula (21) and formula (24), we can get:

[0138]

[0139]

[0140]

[0141]

[0142] Considering μ * (t),ω * (t), θ * (t), σ * From the above formulas (33)-(36), we can get the optimal solution distribution of the dual information collaborative diffusion control strategy as follows:

[0143]

[0144]

[0145]

[0146]

[0147] On the basis of the optimal control strategy solution, by combining the dual information cooperative diffusion control system (10)-(15) and the system's adjoint equations (26)-(31), a dual information cooperative diffusion optimal control system can be constructed to achieve the optimal control of dual information cooperative diffusion.

[0148] In another embodiment, the single information weak attraction strategy refers to taking effective measures to make<S1,S2> The susceptible user knows and becomes interested in Mes1 and Mes2, thus changing the state to<I1,S2> and<S1,I2> .

[0149] In this embodiment, μ(t) is defined as the state transition occurring at time t.<S1,S2> →<I1,S2> The implementation strength of the single information weak attraction control strategy is, ω(t) is the state transition at time t.<S1,S2> →<S1,I2> The implementation intensity of the single information weak attraction control strategy.

[0150] In another embodiment, the dual information strong attraction strategy refers to taking other measures to make the user who is currently in the situation of only having one piece of information, Mes1 or Mes2,<I1,S2> or<S1,I2> The user continues to diffuse another piece of information Mes2 or Mes1, thus changing the state to and

[0151] In this embodiment, θ(t) is defined as the state transition occurring at time t. The implementation strength of the single information weak attraction control strategy, σ(t) is the state transition at time t. The implementation intensity of the single information weak attraction control strategy.

[0152] In another embodiment, the proposed dual-information cooperative diffusion kinetic model and optimal control method are verified by a system simulation method. First, the dynamic evolution results and diffusion trends of the dual-information cooperative diffusion kinetic model are given in different scenarios; then, a sensitivity analysis of the important parameters related to the kinetic model is performed to reveal the influence of different parameters on the model evolution results. Finally, based on the fourth-order Runge-Kutta method, the proposed optimal control strategy for dual-information cooperative diffusion is solved, and the influence of implementing different control strategies on the evolution process of dual-information cooperative diffusion is analyzed.

[0153] We conduct simulation experiments based on the real social network dataset Twitter, which contains real user interaction records on the Twitter social platform. The default parameters used in the simulation experiments are shown in Table 2.

[0154]

[0155] Table 2

[0156] In order to characterize the evolution process of dual information cooperative diffusion, verify the correctness of the dual information cooperative diffusion dynamic model proposed by this method, and further analyze the model evolution process and diffusion trend, we simulated the proposed dynamic model in two scenarios. In scenario 1, we set α = 0.15, β = 0.2, γ = 0.3, η = 0.4, δ = 0.01, then In scenario 2, we set α = 0.05, β = 0.1, γ = 0.2, η = 0.6, δ = 0.05, then We conduct two sets of simulation experiments in the above scenarios to characterize the evolution of the proportion of users in different states over time in the above scenarios, which are called Experimental Case 1 and Case 2 respectively. The experimental results are shown in Figure 3 and Figure 4 shown.

[0157] Figure 3 Given the network in scenario 1<S1,S2> ,<I1,S2> ,<S1,I2> , <r>The evolution of the proportion of state users over time, from Figure 3 We can see that as the time step increases, the diffusion of dual information in the network and The proportion of users in the status showed a gradual increasing trend, and The proportion of status users increased more than |Status users. The proportion of status users shows a trend of first slightly increasing and then decreasing. This shows that over time<S1,S2> Evolution, the dual information gradually spreads in the network and the diffusion range becomes larger and larger. The above experimental results clearly depict the In addition, the accuracy of the prediction results of the trend of the synergistic diffusion of dual information is verified at the same time. When , the number of users with forwarding capabilities in the network gradually increases, and double collaborative diffusion breaks out and continues to spread in the network.

[0158] Figure 4 Given the network in scenario 2<S1,S2> ,<I1,S2> ,<S1,I2> , <r>The evolution of the proportion of state users over time, from Figure 4 We can see that as the time step increases, the diffusion of dual information in the network and The proportion of users in the status showed a trend of increasing first and then gradually decreasing, and The proportion of users in status is greater than Status user.<S1,S2> The proportion of state users shows a gradual increasing trend. This shows that with the evolution of time, the trend of dual information cooperative diffusion in the network has gradually decreased after a slight increase. After a period of time, the scope of dual information cooperative diffusion in the network has gradually decreased. The above experimental results accurately depict the In addition, the above experimental results also verify the accuracy of the prediction results of the trend of double information collaborative diffusion. When , double cooperative diffusion cannot break out in the network and will gradually die out with the evolution of time.

[0159] In another embodiment, in order to explore the influence of different parameters on the information diffusion range in the dual information cooperative diffusion dynamics model, we carried out parameter sensitivity analysis experiments, and the results are as follows: Figure 5 In addition, we simulated the partial correlation coefficients (PRCC) of different parameters in the dynamic model relative to the range of dual information cooperative diffusion, and the results are shown in Figure 6 shown.

[0160] Figure 5 shows the parameters of the dual information cooperative diffusion dynamics model α, β, γ, η, δ, λ in relation to the proportion of users diffusing dual information. Sensitivity analysis results. We can see that with the increase of parameters α, β, γ, η, the proportion of users with dual information diffusion increases significantly, and the influence of γ and η on the proportion of nodes with dual information diffusion is greater than that of α and β. This is because in the dual information cooperative diffusion dynamics model, γ and η are respectively related to the user information state transition. directly related to the state transition. However, α and β are indirectly related to the above state transition. In addition, we can see that the changes of δ and λ have little effect on the proportion of users with dual information diffusion.

[0161] Figure 6 The PRCC analysis results of parameters α, β, γ, η, δ, λ and the proportion of diffuse dual information users are given in . PRCC is a common method for analyzing parameter sensitivity. From the PRCC analysis results, it can be seen that α, β, γ, η, λ are all positively correlated with the proportion of diffuse dual information users, and their increase will lead to an increase in the proportion of diffuse dual information users, and the impact of γ and η on the proportion of diffuse dual information users is greater than that of α and β, and the impact of λ is relatively weak. In addition, δ is negatively correlated with the proportion of diffuse dual information users and has a relatively weak impact on it. The above experimental results are consistent with Figure 5 This is consistent with the experimental results in , which vividly shows the influence of different parameters on the information diffusion range in the dual information cooperative diffusion dynamics model.

[0162] In another embodiment, in order to explore the effects of different control strategies on the collaborative diffusion process of dual information, we conducted the following simulation experiments in scenarios 1 and 2, respectively. Case 3: In scenario 1, only a single information weak attraction strategy is adopted; Case 4: In scenario 1, only a dual information strong attraction strategy is adopted; Case 5: In scenario 1, both a single information weak attraction strategy and a dual information strong attraction strategy are adopted; Case 6: In scenario 2, only a single information weak attraction strategy is adopted; Case 7: In scenario 2, only a dual information strong attraction strategy is adopted; Case 8: In scenario 2, both a single information weak attraction strategy and a dual information strong attraction strategy are adopted. The proportion of dual information users and the distribution of control strategies in different cases are shown in the figure below. Figures 7 to 12 As shown in the figure, Total0 represents the proportion of users who spread double information before taking control measures, and Total represents the proportion of users who spread double information after taking control measures. The corresponding system utility analysis results in Cases 1-8 are as follows: Fig.13 shown.

[0163] from Figure 7 and Figure 8 It can be seen that the implementation of the single information weak attraction strategy and the dual information strong attraction strategy for scenario 1 will cause a significant increase in the proportion of diffuse dual information users, indicating the effectiveness of the proposed control strategy. The increase in the proportion of diffuse dual information users in case 4 is greater than that in case 3, indicating that the control effect of the dual information strong attraction strategy is more obvious than that of the single information weak attraction strategy, which can more directly lead to an increase in the proportion of diffuse dual information users.

[0164] Will Fig. 9 The experimental results and Figure 7 and Figure 8 By comparison, we can see that when the single information weak attraction strategy and the dual information strong attraction strategy are implemented simultaneously, the proportion of users who spread dual information in scenario 1 has increased significantly and quickly maintained a high peak value (0.9). The experimental results in Case 5 fully demonstrate the efficiency of the optimal control strategy we proposed to coordinate the single information weak attraction strategy and the dual information strong attraction strategy.

[0165] from Fig.10 and Fig.11 It can be seen from the above that the implementation of the single information weak attraction strategy and the dual information strong attraction strategy for scenario 2 in case 6 and case 7 respectively will also cause a significant increase in the proportion of users with diffuse dual information, further verifying the effectiveness of the proposed control strategy. Fig.12 The experimental results and Fig.10 and Fig.11 By comparison, we can still find that when both the single information weak attraction strategy and the dual information strong attraction strategy are implemented in Case 8, the proportion of users who spread dual information in Scenario 2 is significantly improved, which fully demonstrates the efficiency of our proposed strategy.

[0166] Fig.13 The analysis results of the system utility (i.e., the objective function value in problem P) in cases 1-8 are given in . It can be clearly seen that, compared with cases 1 and 2 without control measures, cases 3-5 and 6-7 with control measures have obvious improvements in system utility values. It is worth noting that in cases 5 and 8, where both the single information weak attraction strategy and the double information strong attraction strategy are implemented simultaneously, the improvement in system utility values ​​is most obvious. The above experimental results fully verify the correctness and efficiency of the optimal control strategy we solved, which can maximize information diffusion while minimizing control costs.

[0167] In summary, this method establishes a dynamic model of dual information cooperative propagation in social networks and proposes an optimal control method for dual information cooperative propagation. First, for the dual information cooperative propagation process in social networks, a dynamic model based on ordinary differential equations is established to analyze and characterize its propagation evolution law. Through theoretical analysis of the dynamic model, the necessary conditions that determine whether dual information cooperative propagation can break out or disappear in social networks are derived, and its propagation trend is predicted. Two types of dual information propagation process control strategies are proposed, and on this basis, an optimal control system for dual information cooperative propagation is established to achieve effective control of its propagation process.

[0168] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.< / r> < / r> < / r> < / r> < / r> < / r> < / r> < / r> < / r>

Claims

1. A dynamic modeling method for the collaborative diffusion process of dual information in social networks, characterized in that: Based on the two information diffusion pathways of social contact and random contact among users in social networks, Establish a dual information cooperative diffusion dynamics model based on ordinary differential equations to accurately describe the dual information cooperative diffusion process related to the same event in social networks; in, The social contact means that each user in the user set can use the directed edges between him and his neighbors in the social network to achieve directed diffusion of information; The random contact means that each user in the user set will receive some random information sources to achieve information diffusion; The modeling method of the dual information cooperative diffusion dynamics model specifically includes the following steps: S100: Given a social network , where V represents the user set and E represents the set of directed edges; S200: When information related to the same event and When spreading in social networks, , They represent the The proportion of users in Indicates that the user has not received any information and , but it is possible to receive them in the future; Indicates that the user has currently received the information , but no information was received , and may spread information to other users in the social network ; : Indicates that the user has currently received the information , but no information was received Similarly, users may spread the information they receive to other users in the social network. ; Indicates that the user has currently received the information and , and receive information Earlier than information In addition, users may spread information to other users in the social network and ; Indicates that the user has currently received the information and , and receive information Earlier than information , and users are likely to spread information to other users in the social network and ; The user is currently viewing the information and Lose interest, are unwilling to receive them, and do not participate in their diffusion process; S300: Establish about and The dual information cooperative diffusion dynamics model is: （1） （2） （3） （4） （5） （6） The initial values ​​of the model are: （7） The constraints of the model are: （8） in, , , and They represent the probability of users receiving information from the social contact layer and the random contact layer, represents the probability of a user's state transition due to losing interest in information, represents the probability of state transition due to renewed interest in information by the user, α express Status User received the message Later transferred to The probability of the state, β represents Status User received the message Later transferred to The probability of the state, γ represents Status User received the message Later transferred to The probability of the state, η represents Status User received the message Later transferred to Probability of state; The method for predicting the trend of double information cooperative diffusion based on the double information cooperative diffusion dynamics model comprises the following steps: S400: Extracting the forwarding and The sub-terms of capacity form the following diffusion equation: （9） in Satisfies the following matrix: ； in, ； ； S500: Calculated and The derivative in the zero equilibrium state is: ； in, , ; S600: Construct the following characteristic equation: ； By solving the characteristic roots of the above characteristic equation, we can calculate and Joint basic reproduction number of cooperative diffusion : ； Among them Indicated in and The degree of influence of users with forwarding capabilities on other users in the collaborative diffusion process; S700: According to the combined basic regeneration number judge and Whether the coordinated diffusion of is breaking out in social networks; The optimal control method of dual information collaborative diffusion based on the dual information collaborative diffusion dynamics model comprises the following steps: S800: Propose different information diffusion control strategies for users with different information status; S900: Establishment of a dual information cooperative diffusion control dynamics system; S1000: Based on optimal control theory, solving the optimal solution distribution of the information diffusion control strategy over time.

2. According to the method of claim 1, the step S700 further comprises: S701: If , the number of users with forwarding capabilities in social networks will gradually decrease, and The coordinated diffusion of information cannot break out and will gradually die out over time. Information will eventually disappear in the social network and reach a stable state. S702: If , the number of users with forwarding capabilities in social networks will gradually increase, and The coordinated diffusion of will break out and continue to spread in social networks. The bigger it is, the more obvious its tendency to explode is.

3. According to the method described in claim 1, the information diffusion control strategy includes a single information weak attraction strategy and a double information strong attraction strategy.

4. According to the method of claim 3, the single information weak attraction strategy refers to taking effective measures to make The user is aware of the susceptible status and responds to and Generate interest, thus changing the state to and .

5. According to the method of claim 3, the dual information strong attraction strategy refers to the situation where the user currently only has or When a message is received, other measures are taken to or Users continue to respond to another message or Diffusion, thus changing the state to and .

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