Nonlinear rumor propagation suppression model and construction method thereof

Abstract

A nonlinear rumor propagation inhibition model is composed of a susceptible user model F (S, I) and an infected user model G (S, I) shown in a formula (1), the construction method of the nonlinear rumor propagation suppression model comprises the steps of dividing online social network crowds, spreading rumors, determining balance points of the suppression model, determining stability conditions of the balance points of the suppression model and constructing the nonlinear rumor propagation suppression model. The rumor propagation process in the online social network is described by adopting the nonlinear incidence rate, the technical problem that the rumor propagation process cannot be accurately described by the linear incidence rate in the prior art is solved, and the complex rumor propagation process caused by the education level, trust and forgetting mechanism is clearly described. The built rumor propagation inhibition model is subjected to a computer simulation experiment, and the result shows that the stable value of the infected user I (x, t) is 0, and the rumor in the online social network disappears. The model can be used for suppressing and eliminating rumors in an online social network.

Description

Technical Field

[0001] The present invention belongs to the field of computer application technology, and specifically relates to information dissemination. Background Art

[0002] In recent years, with the popularization of the Internet and the development of online social media, communication between people has become more and more convenient. More frequent communication has made online social networks full of various information, including various rumors. In real online social networks, rumors continue to spread in various information, making it difficult for users to distinguish between true and false, thereby expanding their influence. Especially when major events occur, due to the strong incitement of rumors, they can spread quickly and cause panic among the people, thus causing adverse effects on the entire society. Faced with online rumors, some users choose to blindly follow the trend and become supporters and spreaders of rumors, while other users realize that the information they spread is untrue, so they will not be affected by the rumors and will not continue to spread them. According to the propagation characteristics of rumors and the classification of users in the rumor system, a rumor propagation model is constructed, and the rumor propagation characteristics are analyzed to provide a theoretical basis for rumor control.

[0003] In 1965, Daley and Kendall first proposed a rumor propagation model, known as the DK model, and used random processes to analyze it. The model depicts the unique propagation characteristics of rumors and has a profound inspiration for subsequent scholars. In 1973, Maki and Thompson changed the propagation mechanism of the DK model and proposed the Maki-Thomson model, known as the MT model, and used mathematical theory to analyze it. This model is superior to the DK model and can be regarded as an improvement and enhancement of the DK model. Since then, the development of complex network theory has led to in-depth research on the dynamics of rumor propagation. Social group factors such as forgetting, refuting rumors, revealing the truth, friendships, and fermentation period lags have led to more in-depth research on the dynamics of rumor propagation. Summary of the invention

[0004] A technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned technologies and provide a nonlinear rumor propagation suppression model that can suppress and eliminate rumors in online social networks.

[0005] Another technical problem to be solved by the present invention is to provide a construction method with a high suppression rate for a nonlinear rumor propagation suppression model.

[0006] The technical solution adopted to solve the above technical problems is:

[0007] The nonlinear rumor propagation suppression model consists of the susceptible user model F(S,I) and the infected user model G(S,I) as shown in formula (1):

[0008]

[0009] In the susceptible user model F(S,I), S(x,t) represents the susceptible user density when the distance is x and the time is t, S t represents the partial derivative of susceptible user S(x,t) with respect to t, d S ΔS(x,t) represents the spread of susceptible users, d S is the diffusion coefficient of susceptible users, Δ represents the Laplace operator, θ is the entry rate of susceptible users, f(S,I) represents that susceptible users become infected users after being affected by rumors, β is the propagation coefficient of nonlinear propagation rate, α is the user's psychological adjustment factor, g1(S) represents the exit rate of susceptible users, μ is the exit rate coefficient of susceptible users and infected users, and L represents the maximum distance of online social networks.

[0010] In the infected user model G(S,I), I(x,t) represents the density of infected users at a distance of x and a time of t. t represents the partial derivative of the infected user I(x,t) with respect to t, d I ΔI(x,t) represents the spread of infected users, d I is the diffusion coefficient of infected users, g2(I) represents the exit rate of infected users, S0(x) represents the initial density distribution of susceptible users, I0(x) represents the initial density distribution of infected users, and on the boundary:

[0011]

[0012]

[0013] In the nonlinear rumor propagation suppression model of formula (1), the d S d I The value range of θ, β, α, μ, S0(x), and I0(x) is (0,1], and the value range of L is [1,5].

[0014] In the nonlinear rumor propagation suppression model of formula (1), the d S The best value is 0.5, d I The best value is 0.5, the best value of θ is 0.3, the best value of β is 0.39, the best value of α is 0.5, the best value of μ is 0.5, the best value of S0(x) is 0.5, the best value of I0(x) is 0.5, and the best value of L is 3.

[0015] The construction method of the nonlinear rumor propagation suppression model shown in formula (1) consists of the following steps:

[0016] (1) Segmentation of online social network populations

[0017] The people in the online social network are divided into susceptible users S(x,t) and infected users I(x,t).

[0018] (2) The process of spreading rumors

[0019] People in the online social network enter susceptible users S(x, t) at an entry rate of θ. After susceptible users S(x, t) are exposed to rumors, they are converted to susceptible users at a nonlinear conversion rate Transformed into infected users I(x, t), susceptible users S(x, t) are pushed out at a linear rate μS(x, t), infected users I(x, t) exit at a linear rate μI(x, t), susceptible users S(x, t) exit at a diffusion coefficient d S Free diffusion, infected users I(x,t) with diffusion coefficient d I Free diffusion.

[0020] (3) Determine the equilibrium point of the suppression model

[0021] 1) Establish a balance point without rumor propagation

[0022] Construct the rumor-free equilibrium point E0 according to the following formula:

[0023]

[0024] 2) Establish a balance point for rumor propagation

[0025] When αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 = 0, construct two identical rumor propagation equilibrium points E1; when αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 When >0, two different rumor propagation equilibrium points E2 and E3 are constructed:

[0026]

[0027]

[0028] (4) Determine the stability conditions for suppressing the equilibrium point of the model

[0029] 1) Construct the equilibrium point E of the suppression model * The linearization operator at

[0030] The inhibition model equilibrium point E is constructed as follows * The linearization operator L(E * ):

[0031]

[0032] 2) Construct the equilibrium point E of the suppression model * The eigenvalue at

[0033] The inhibition model equilibrium point E is constructed as follows * The eigenvalue M at i :

[0034]

[0035] Among them, ρ i is the eigenvalue of the -Δ operator under homogeneous Neumann boundary conditions, i is a finite positive integer, is the corresponding eigenvector.

[0036] 3) Determine the stability conditions of the equilibrium point

[0037] The stability conditions of the equilibrium point include:

[0038] αμ 2 -βθ<0;

[0039] (αμ 2 -βθ) 2 -4βμ 3 >0 and

[0040]

[0041] 4) Determine the stability condition of the equilibrium point E0 without rumor propagation

[0042] When αμ 2 When -βθ<0, the equilibrium point E0 is globally asymptotically stable.

[0043] 5) Determine the stability condition of rumor propagation equilibrium point E3

[0044] When αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 >0 and When , the equilibrium point E3 is locally asymptotically stable.

[0045] (5) Constructing a nonlinear rumor propagation suppression model

[0046] According to steps (1), (2), (3), and (4), a nonlinear rumor propagation suppression model is constructed, as shown in formula (1).

[0047] The beneficial effects of the present invention are:

[0048] The present invention divides people in online social networks into two categories, determines the rumor propagation process, determines the equilibrium point of the suppression model, and determines the stability condition of the equilibrium point of the suppression model, and constructs a rumor propagation suppression model. Since the present invention uses nonlinear incidence to describe the rumor propagation process in online social networks, it solves the technical problem that the linear incidence cannot accurately describe the rumor propagation process in the prior art, and can more clearly describe the complex process of rumor propagation caused by education level, trust mechanism, and forgetting mechanism. The rumor propagation suppression model constructed by the present invention was used to carry out a computer laboratory simulation experiment. The experimental results show that the infected user I(x, t) tends to be stable, the stable value is 0, and the rumor in the online social network disappears. The model can be used to suppress and eliminate rumors in online social networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of Example 1 of the present invention.

[0050] Figure 2 1 is a spatiotemporal sequence diagram of susceptible users at the equilibrium point E0 without rumor propagation in Example 1 of the present invention.

[0051] Figure 3 It is a spatiotemporal sequence diagram of infected users at the equilibrium point E0 without rumor propagation in Example 1 of the present invention.

[0052] Figure 4 It is a spatiotemporal sequence diagram of susceptible users at the rumor propagation equilibrium point E3 of Example 1 of the present invention.

[0053] Figure 5 It is a spatiotemporal sequence diagram of infected users at the rumor propagation equilibrium point E3 of Example 1 of the present invention. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the accompanying drawings and examples, but the present invention is not limited to the following embodiments.

[0055] Example 1

[0056] The nonlinear rumor propagation suppression model of this embodiment is composed of the susceptible user model F(S, I) and the infected user model G(S, I) shown in formula (1):

[0057]

[0058] In the susceptible user model F(S,I), S(x,t) represents the susceptible user density when the distance is x and the time is t, S t represents the partial derivative of susceptible user S(x,t) with respect to t, d S ΔS(x,t) represents the spread of susceptible users, d Sis the diffusion coefficient of susceptible users, Δ represents the Laplace operator, θ is the entry rate of susceptible users, f(S,I) represents the susceptible users becoming infected users after being affected by rumors, β is the propagation coefficient of nonlinear propagation rate, α is the user's psychological adjustment factor, g1(S) represents the exit rate of susceptible users, μ is the exit rate coefficient between susceptible users and infected users, and L represents the maximum distance of the online social network; d S d I The value ranges of θ, β, α, μ, S0(x), and I0(x) are (0,1], and the value range of L is [1,5]. S The value is 0.5, d I The value is 0.5, θ is 0.3, β is 0.39, α is 0.5, μ is 0.5, S0(x) is 0.5, I0(x) is 0.5, and L is 3.

[0059] In the infected user model G(S,I), I(x,t) represents the density of infected users at a distance of x and a time of t. t represents the partial derivative of the infected user I(x,t) with respect to t, d I ΔI(x,t) represents the spread of infected users, d I is the diffusion coefficient of infected users, g2(I) represents the exit rate of infected users, S0(x) represents the initial density distribution of susceptible users, I0(x) represents the initial density distribution of infected users, and on the boundary:

[0060]

[0061] The method for constructing the nonlinear rumor propagation suppression model of this embodiment consists of the following steps (eg Figure 1 shown):

[0062] (1) Segmentation of online social network populations

[0063] The people in the online social network are divided into susceptible users S(x,t) and infected users I(x,t).

[0064] (2) The process of spreading rumors

[0065] People in the online social network enter susceptible users S(x, t) at an entry rate of θ. After susceptible users S(x, t) are exposed to rumors, they are converted to susceptible users at a nonlinear conversion rate Transformed into infected users I(x, t), susceptible users S(x, t) are pushed out at a linear rate μS(x, t), infected users I(x, t) exit at a linear rate μI(x, t), susceptible users S(x, t) exit at a diffusion coefficient d S Free diffusion, infected users I(x,t) with diffusion coefficient d IFree diffusion.

[0066] (3) Determine the equilibrium point of the suppression model

[0067] 1) Establish a balance point without rumor propagation

[0068] Construct the rumor-free equilibrium point E0 according to the following formula:

[0069]

[0070] 2) Establish a balance point for rumor propagation

[0071] When αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 = 0, construct two identical rumor propagation equilibrium points E1; when αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 When >0, two different rumor propagation equilibrium points E2 and E3 are constructed:

[0072]

[0073] (4) Determine the stability conditions for suppressing the equilibrium point of the model

[0074] 1) Construct the equilibrium point E of the suppression model * The linearization operator at

[0075] The inhibition model equilibrium point E is constructed as follows * The linearization operator L(E * ):

[0076]

[0077] 2) Construct the equilibrium point E of the suppression model * The eigenvalue at

[0078] The inhibition model equilibrium point E is constructed as follows * The eigenvalue M at i :

[0079]

[0080] Among them, ρ i is the eigenvalue of the -Δ operator under homogeneous Neumann boundary conditions, i is a finite positive integer, is the corresponding eigenvector.

[0081] 3) Determine the stability conditions of the equilibrium point

[0082] The stability conditions of the equilibrium point include:

[0083] αμ 2 -βθ<0

[0084] (αμ 2 -βθ) 2 -4βμ 3 >0 and

[0085]

[0086] 4) Determine the stability condition of the equilibrium point E0 without rumor propagation

[0087] When αμ 2 When -βθ<0, the equilibrium point E0 is globally asymptotically stable.

[0088] 5) Determine the stability condition of rumor propagation equilibrium point E3

[0089] When αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 >0 and When , the equilibrium point E3 is locally asymptotically stable.

[0090] (5) Constructing a nonlinear rumor propagation suppression model

[0091] According to steps (1), (2), (3), and (4), a nonlinear rumor propagation suppression model as shown in formula (1) is constructed.

[0092] Example 2

[0093] The nonlinear rumor propagation suppression model of this embodiment is composed of the susceptible user model F(S, I) and the infected user model G(S, I) shown in formula (1):

[0094] The expression of the nonlinear rumor propagation suppression model formula (1) is the same as that in Example 1.

[0095] In the susceptible user model F(S,I) of formula (1), d S d I The value ranges of θ, β, α, μ, S0(x), and I0(x) are (0,1], and the value range of L is [1,5]. S The value is 0.1, d I The value of is 0.1, the value of θ is 0.1, the value of β is 0.1, the value of α is 0.1, the value of μ is 0.1, the value of S0(x) is 0.1, the value of I0(x) is 0.1, and the value of L is 1. The meanings and values ​​of other variables, coefficients, and parameters are the same as those in Example 1.

[0096] In the infected user model G(S, I) of formula (1), the meanings and values ​​of variables, coefficients, and parameters are the same as those in Example 1.

[0097] In the method for constructing a nonlinear rumor propagation suppression model, the meanings of variables, coefficients, and parameters are the same as those in Example 1, and the values ​​of coefficients and parameters are the same as those in Example 2. A rumor propagation suppression model is constructed as shown in Formula (1).

[0098] Example 3

[0099] The nonlinear rumor propagation suppression model of this embodiment is composed of the susceptible user model F(S, I) and the infected user model G(S, I) shown in formula (1):

[0100] The expression of the nonlinear rumor propagation suppression model formula (1) is the same as that in Example 1.

[0101] In the susceptible user model F(S,I) of formula (1), d S d I The value ranges of θ, β, α, μ, S0(x), and I0(x) are (0,1], and the value range of L is [1,5]. S The value is 1, d I The value of is 1, the value of θ is 1, the value of β is 1, the value of α is 1, the value of μ is 1, the value of S0(x) is 1, the value of I0(x) is 1, and the value of L is 5. The meanings and values ​​of other variables, coefficients, and parameters are the same as those in Example 1.

[0102] In the infected user model G(S, I) of formula (1), the meanings and values ​​of variables, coefficients, and parameters are the same as those in Example 1.

[0103] In the method for constructing a nonlinear rumor propagation suppression model, the meanings of variables, coefficients, and parameters are the same as those in Example 1, and the values ​​of coefficients and parameters are the same as those in Example 3. A rumor propagation suppression model is constructed as shown in Formula (1).

[0104] In order to verify the beneficial effects of the present invention, a simulation experiment was carried out using Example 1 of the present invention. The experimental results are shown in FIG. Figure 2-Figure 5 .

[0105] exist Figure 2 In the above example, the horizontal axis represents time t, the vertical axis represents space x, and the vertical axis represents susceptible users S(x,t). Figure 2 It can be seen that after a long period of behavior, the susceptible user S(x,t) tends to be stable, and the stable value is 1.15.

[0106] exist Figure 3In the above example, the horizontal axis represents time t, the vertical axis represents space x, and the vertical axis represents the number of users infected by the rumor I(x,t). Figure 3 It can be seen that after a long period of behavior, the number of infected users I(x,t) tends to be stable, and the stable value is 0, indicating that the rumors in the online social network disappear.

[0107] exist Figure 4 In the above example, the horizontal axis represents time t, the vertical axis represents space x, and the vertical axis represents the number of users infected by the rumor I(x,t). Figure 4 It can be seen that after a long period of behavior, the number of infected users S(x,t) tends to be stable, with a stable value of 0.67.

[0108] exist Figure 5 In the above example, the horizontal axis represents time t, the vertical axis represents space x, and the vertical axis represents the number of users infected by the rumor I(x,t). Figure 5 It can be seen that after a long period of behavior, the number of infected users I(x,t) tends to be stable, with a stable value of 0.83, indicating that rumors persist in online social networks.

Claims

1. A nonlinear rumor propagation suppression model, characterized by The model consists of the susceptible user model F(S,I) and the infected user model G(S,I) as shown in formula (1): In the susceptible user model F(S,I), S(x,t) represents the susceptible user density when the distance is x and the time is t, S t represents the partial derivative of susceptible user S(x,t) with respect to t, d S ΔS(x,t) represents the spread of susceptible users, d S is the diffusion coefficient of susceptible users, Δ represents the Laplace operator, θ is the entry rate of susceptible users, f(S,I) represents the susceptible users becoming infected users after being affected by rumors, β is the propagation coefficient of nonlinear propagation rate, α is the psychological adjustment factor of users, g1(S) represents the exit rate of susceptible users, μ is the exit rate coefficient of susceptible users and infected users, and L represents the maximum distance of online social networks; In the infected user model G(S,I), I(x,t) represents the infected user density when the distance is x and the time is t. t represents the partial derivative of the infected user I(x,t) with respect to t, d I ΔI(x,t) represents the spread of infected users, d I is the diffusion coefficient of infected users, g2(I) represents the exit rate of infected users, S0(x) represents the initial density distribution of susceptible users, I0(x) represents the initial density distribution of infected users, and on the boundary:

2. The nonlinear rumor propagation suppression model according to claim 1 is characterized in that: In the nonlinear rumor propagation suppression model of formula (1), the d S ,d I The value range of θ, β, α, μ, S0(x), and I0(x) is (0,1], and the value range of L is [1,5].

3. The nonlinear rumor propagation suppression model according to claim 1 or 2, characterized in that: In the nonlinear rumor propagation suppression model of formula (1), the d S The value is 0.5, d I The value is 0.5, θ is 0.3, β is 0.39, α is 0.5, μ is 0.5, S0(x) is 0.5, I0(x) is 0.5, and L is 3.

4. A method for constructing a nonlinear rumor propagation suppression model as claimed in claim 1, characterized in that It consists of the following steps: (1) Segmentation of online social network populations Divide the people in online social networks into susceptible users S(x,t) and infected users I(x,t); (2) The process of spreading rumors People in the online social network enter susceptible users S(x, t) at an entry rate of θ. After susceptible users S(x, t) are exposed to rumors, they are converted to susceptible users at a nonlinear conversion rate Transformed into infected users I(x, t), susceptible users S(x, t) are pushed out at a linear rate μS(x, t), infected users I(x, t) exit at a linear rate μI(x, t), susceptible users S(x, t) exit at a diffusion coefficient d S Free diffusion, infected users I(x,t) with diffusion coefficient d I Free diffusion; (3) Determine the equilibrium point of the suppression model 1) Establish a balance point without rumor propagation Construct the rumor-free equilibrium point E0 according to the following formula: 2) Establish a balance point for rumor propagation When αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 = 0, construct two identical rumor propagation equilibrium points E1; when αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 When >0, two different rumor propagation equilibrium points E2 and E3 are constructed: (4) Determine the stability conditions for suppressing the equilibrium point of the model 1) Construct the equilibrium point E of the suppression model * The linearization operator at The inhibition model equilibrium point E is constructed as follows * The linearization operator L(E * ): 2) Construct the equilibrium point E of the suppression model * The eigenvalue at The inhibition model equilibrium point E is constructed as follows * The eigenvalue M at i : Among them, ρ i is the eigenvalue of the -Δ operator under homogeneous Neumann boundary conditions, i is a finite positive integer, is the corresponding eigenvector; 3) Determine the stability conditions of the equilibrium point The stability conditions of the equilibrium point include: am 2 -βθ<0, (αμ 2 -βθ) 2 -4βμ 3 >0 and 4) Determine the stability condition of the equilibrium point E0 without rumor propagation When αμ 2 When -βθ<0, the equilibrium point E0 is globally asymptotically stable; 5) Determine the stability condition of rumor propagation equilibrium point E3 When αμ 2 -βθ<0,(αμ 2 -βθ) 2 -4βμ 3 >0 and When , the equilibrium point E3 is locally asymptotically stable; (5) Constructing a nonlinear rumor propagation suppression model According to steps (1), (2), (3), and (4), a nonlinear rumor propagation suppression model is constructed, as shown in formula (1).

Images