Double-viewpoint network consensus forming method based on fixed execution characteristics and dynamic interaction

Abstract

A double-viewpoint network consensus forming method based on fixed handling characteristics and dynamic interaction belongs to the technical field of social network analysis and viewpoint dynamics, and comprises the following steps: step 1, constructing a time-varying influence network model with a competition and cooperation relationship; 2, establishing a double-viewpoint dynamic model; 3, performing individual classification and network reconstruction; step 4, consensus formation and convergence determination; according to the method, in a time-varying social network with a cooperation and adversarial relationship, sufficient conditions of viewpoint consensus and convergence are determined through graph theory analysis, and an influence criterion of the classification number of amnesia individuals and non-amnesia individuals on individual consensus under each theme is determined; according to the method, the rule that fixed individuals regulate and control collective convergence dynamics through the multi-theme interaction matrix can be accurately revealed, and effective technical support is provided for viewpoint evolution prediction and consensus guidance in a complex social network.

Description

Technical Field

[0001] This invention relates to the fields of social network analysis and opinion dynamics, specifically to a method for forming consensus in a dual-opinion network based on stubbornness and dynamic interaction. Background Technology

[0002] In the digital age, the ubiquitous reach and instant interactivity of social networks have made the formation, evolution, and diffusion of public opinion a core force in reshaping social structures, guiding public decision-making, and influencing cultural trends. From public opinion dissemination and policy promotion to commercial marketing and public event response, the research findings of opinion dynamics have permeated many key areas such as social governance and economic operation, and its theoretical value and application potential are increasingly prominent. As an interdisciplinary field integrating sociology, psychology, mathematics, computer science, and communication studies, opinion dynamics aims to reveal the convergence, divergence, or stabilization mechanisms of individual opinions within a group, and to explore the complex interaction patterns between individual cognition, social influence, and environmental factors. In online groups, individuals update their opinions through iterative interactions with neighboring individuals; the dynamic nature of this process constitutes the core logic of opinion dissemination.

[0003] However, interpersonal interactions in real-world social networks are far more complex than simple cooperative or competitive relationships. On the same issue, an individual may form cooperative relationships with some groups, sharing viewpoints and resources, while simultaneously experiencing cognitive conflict and competition with others. This intertwined relationship of cooperation and antagonism makes the difference between an individual's private viewpoint and their expressed viewpoint increasingly significant. Existing viewpoint evolution models are mostly divided into consensus models based on complete cooperation and polarization theories based on complete competition, which struggle to characterize the complex relationships of cooperation and competition in real-world social networks. Most studies fail to distinguish between an individual's true private viewpoint and their publicly expressed viewpoint, failing to explain phenomena such as "inner conviction but refusal to compromise after public expression." Furthermore, existing models often assume a fixed interaction intensity, failing to adequately consider changes in interaction intensity in dynamic environments, and lack in-depth analysis of the coupling effect between the cognitive rigidity of stubborn individuals and the strategic expression of ordinary individuals.

[0004] Therefore, there is an urgent need to construct a viewpoint dynamics model that can take into account the differences between two viewpoints, time-varying network structures, cooperative and antagonistic relationships, and the influence of stubborn individuals, in order to accurately reveal the evolutionary laws of viewpoints in complex social networks. Summary of the Invention

[0005] The purpose of this invention is to provide a method for forming consensus in a dual-viewpoint network based on stubbornness and dynamic interaction, so as to solve the problem that existing technologies cannot accurately characterize the evolution of viewpoints in complex social networks.

[0006] The technical solution of this invention is: a method for forming consensus in a dual-viewpoint network based on stubbornness and dynamic interaction, the method comprising the following steps:

[0007] Step 1, Construct a time-varying influence network model: Use a signed directed graph to describe the interpersonal interactions and interdependencies among individuals in the social network, and define the time-varying influence matrix. The matrix represents trust relationships, where the positive and negative values ​​of the matrix elements correspond to cooperation and antagonism, and satisfy the properties of row randomness and strong connectivity.

[0008] Step 2, establish a dual-viewpoint dynamics model: define an individual's private viewpoint and expressed viewpoint, where the private viewpoint is the individual's true internal viewpoint, and the expressed viewpoint is the external viewpoint that the individual transmits to neighboring individuals. Based on individual stubbornness and the resilience of group viewpoint pressure, establish viewpoint updating rules and the competitive and cooperative relationships between individuals.

[0009] Step 3, Individual Classification and Network Reconstruction: Individuals in the network are classified into forgetful individuals and non-forgetful individuals. Forgetful individuals are neither stubborn nor affected by stubborn individuals, while non-forgetful individuals are either stubborn individuals or individuals affected by stubborn individuals. The time-varying influence matrix is ​​reconstructed based on this classification.

[0010] Step 4, consensus formation and convergence determination: based on the reconstructed network structure, combined with matrix structural balance analysis.

[0011] Furthermore, step 1 is specifically as follows:

[0012] Using a signed directed graph Describe social networks, in which For a set of individual nodes, Let be a set of directed edges. This is the edge weight matrix; edges Represents an individual For individuals There is an impact, and the weight is significant. Positive values ​​indicate cooperation, and negative values ​​indicate competition; Time-varying influence matrix Satisfying row randomness and strong connectivity ensures effective information transmission within the network; the boosting method is used to expand the dimensionality of the cooperative-competitive network.

[0013] Individual Influence Matrix The breakdown is as follows:

[0014]

[0015] in,

[0016]

[0017]

[0018] off-diagonal matrix Decomposed into

[0019]

[0020]

[0021] in, and Each and the individual A set of neighboring individuals with cooperative relationships and individuals A set of neighboring individuals that are in competition with each other. For individuals in the evolution of private viewpoints Individual The influence weight.

[0022] Furthermore, step 2 is detailed as follows:

[0023] Define individual Private viewpoint (True inner viewpoint) and expressing viewpoints (Regarding the external communication of viewpoints), the update rules for both are as follows:

[0024] Private viewpoint updates: Taking into account the private viewpoints of cooperating neighbors, the persistence of one's own initial viewpoint, and the impact of competing neighbors' expressed viewpoints, this is achieved through influence sensitivity. Modulate the intensity of neighborhood influence. It represents the degree to which an individual adheres to their initial viewpoint;

[0025] Expression of updated viewpoints: formed based on individual private opinions and neighbor feedback, and strengthened by the pressure of group viewpoints. Balancing one's own private perspective with the influence of the group, The larger the value, the more inclined the individual is to insist on expressing their own views to the outside world;

[0026] The resulting dual-viewpoint dynamic model is as follows:

[0027]

[0028] in, For individuals in the process of expressing viewpoints evolving Individual The influence weight.

[0029] Furthermore, step 3 is specifically as follows:

[0030] Based on the behavioral characteristics and influence mechanisms of individuals in the process of viewpoint evolution, a clear individual classification criterion is established to accurately divide all individuals in the network into two categories: forgetful individuals and non-forgetful individuals. The specific definitions and judgment logic are as follows:

[0031] Forgetful individuals: neither stubborn ( It is also not affected by stubborn individuals, and there is no opinion transmission path from stubborn individuals to this type of individual;

[0032] Non-forgetful individuals: including stubborn individuals ( There is a viewpoint transmission path from the stubborn individual to individuals influenced by the stubborn individual;

[0033] Based on the above classification, individuals in the network are divided into forgetful individuals and non-forgetful individuals. Forgetful individuals are neither stubborn nor affected by stubborn individuals, while non-forgetful individuals are either stubborn individuals or individuals affected by stubborn individuals. The time-varying influence matrix is ​​reconstructed based on this classification.

[0034] When both non-forgetful and forgetful individuals exist in a two-viewpoint dynamics model, in a time-varying influence network... In the process, non-forgetful individuals and forgetful individuals are renumbered as follows: and Of these, the number of non-amnesiac individuals was... The number of forgetful individuals is ,Right now If all individuals are reordered according to the categories of non-forgetful and forgetful individuals, the diagonal matrix is ​​represented as:

[0035]

[0036] in, Based on the reordering of non-forgetful and forgetful individuals, the time-varying influence matrix Rewritten as:

[0037] .

[0038] Furthermore, step 4 is specifically as follows:

[0039] For network reconstruction A non-forgetful individual, A heterogeneous network of forgetful individuals, with submatrices corresponding to each forgetful individual. Based on the structural balance as the core dividing criterion, the consensus formation rules of private viewpoints and expressed viewpoints are derived in two scenarios, while the convergence characteristics of non-forgetful individuals are clarified:

[0040] when When the structure is unbalanced, and the time-varying influence matrix sequence To achieve consistent joint strong connectivity and pressure influence matrix partitioning and Having the same non-zero element distribution and satisfying the row stochastic property requirement: the private views and expressed views of forgetful individuals reach zero consistency, forming a neutral consensus; the two views of non-forgetful individuals converge to a unified stable value;

[0041] when When the structure is in equilibrium, and the time-varying influence matrix sequence To achieve consistent joint strong connectivity and pressure influence matrix partitioning and With the same non-zero element distribution, the private views and expressed views of forgetful individuals form a polarized consensus, that is, all forgetful individuals are eventually divided into two opposing groups. Views within the same group tend to be consistent, while views between different groups tend to be opposite, which is consistent with the network interaction logic of cooperation and confrontation mentioned above; the dual views of non-forgetful individuals converge to a unified stable value.

[0042] All individuals in the network are non-forgetful (including stubborn individuals and individuals influenced by stubborn individuals), and the time-varying influence matrix sequence... For consistent joint strong connectivity, pressure influence matrix and Having the same distribution of non-zero elements, and the initial viewpoint At the same time, it satisfies the requirement of row randomness, ensuring that the opinion values ​​of all individuals remain within the initial interval. Furthermore, the convergence process is exponential, exhibiting a relatively fast convergence speed, which aligns with the evolutionary characteristics of real-world social networks.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] This invention, by distinguishing between private viewpoints and expressed viewpoints, better reflects the reality that there is a difference between an individual's "inner thoughts" and "public statements" in society; by considering time-varying influence networks and the hybrid relationship of cooperation and confrontation, it accurately portrays the complex interactions between individuals in a dynamic social environment; by incorporating the influence mechanism of stubborn individuals, it reveals the differentiated consensus formation patterns between forgetful and non-forgetful individuals; and by providing clear consensus convergence conditions, it offers an operable technical solution for guiding viewpoints and regulating public opinion in social networks. Attached Figure Description

[0045] Figure 1 The flowchart of the dual-viewpoint network consensus formation method based on stubbornness and dynamic interaction provided by the present invention is shown.

[0046] Figure 2 This is a schematic diagram of the structural balance matrix.

[0047] Figure 3 This is a schematic diagram of a structurally unbalanced matrix.

[0048] Figure 4 In Example 1 A schematic diagram illustrating the evolution of opinions in forgetful individuals when the structure is unbalanced.

[0049] Figure 5 In Example 1 A schematic diagram of the evolution of opinions among non-amnesiac individuals when the structure is unbalanced.

[0050] Figure 6 In Example 2 A schematic diagram illustrating the evolution of opinions in forgetful individuals when the structure is in equilibrium.

[0051] Figure 7 In Example 2 A schematic diagram of the evolution of opinions of non-amnesiac individuals when the structure is in equilibrium.

[0052] Figure 8 This is a schematic diagram illustrating the evolution of individual opinions in Example 3 when the social network does not contain forgetful individuals. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The specific process is as follows: Figure 1 As shown.

[0054] Step 1, using a signed directed graph Describe social networks, in which For a set of individual nodes, Let be a set of directed edges. This is the edge weight matrix; edges Represents an individual For individuals There is an impact, and the weight is significant. Positive values ​​indicate cooperation, and negative values ​​indicate competition; Time-varying influence matrix Satisfying row-randomness and strong connectivity ensures efficient information transmission within the network; employing a boosting method to expand the dimensionality of the cooperative-competitive network; and adjusting the individual influence matrix. The breakdown is as follows:

[0055]

[0056] in,

[0057]

[0058]

[0059] off-diagonal matrix Decomposed into

[0060]

[0061] .

[0062] Step 2, Define Individual Private viewpoint (True inner viewpoint) and expressing viewpoints (Regarding the external communication of viewpoints), the update rules for both are as follows:

[0063] Private viewpoint updates: Taking into account the private viewpoints of cooperating neighbors, the persistence of one's own initial viewpoint, and the impact of competing neighbors' expressed viewpoints, this is achieved through influence sensitivity. Modulate the intensity of neighborhood influence. It represents the degree to which an individual adheres to their initial viewpoint;

[0064] Expression of updated viewpoints: formed based on individual private opinions and neighbor feedback, and strengthened by the pressure of group viewpoints. Balancing one's own private perspective with the influence of the group, The larger the value, the more inclined the individual is to insist on expressing their own views to the outside world;

[0065] The resulting dual-viewpoint dynamic model is as follows:

[0066]

[0067] in, and Each and the individual A set of neighboring individuals with cooperative relationships and individuals A set of neighboring individuals that are in competition with each other. For individuals in the evolution of private viewpoints Individual Influence weight, For individuals in the process of expressing viewpoints evolving Individual The influence weight.

[0068] Step 3: Based on the behavioral characteristics and influence mechanisms of individuals in the process of viewpoint evolution, establish clear individual classification criteria to accurately divide all individuals in the network into two categories: forgetful individuals and non-forgetful individuals. The specific definitions and judgment logic are as follows:

[0069] Forgetful individuals: neither stubborn ( It is also not affected by stubborn individuals, and there is no opinion transmission path from stubborn individuals to this type of individual;

[0070] Non-forgetful individuals: including stubborn individuals ( There is a viewpoint transmission path from the stubborn individual to the individual influenced by the stubborn individual.

[0071] Based on the above classification, individuals in the network are divided into forgetful individuals and non-forgetful individuals. Forgetful individuals are neither stubborn nor affected by stubborn individuals, while non-forgetful individuals are either stubborn individuals or individuals affected by stubborn individuals. The time-varying influence matrix is ​​reconstructed based on this classification.

[0072] When both non-forgetful and forgetful individuals exist in a two-viewpoint dynamics model, in a time-varying influence network... In the process, non-forgetful individuals and forgetful individuals are renumbered as follows: and Of these, the number of non-amnesiac individuals was... The number of forgetful individuals is ,Right now If all individuals are reordered according to the categories of non-forgetful and forgetful individuals, the diagonal matrix can be represented as:

[0073]

[0074] in, Based on the reordering of non-forgetful and forgetful individuals, the time-varying influence matrix It can be rewritten as:

[0075] .

[0076] Step 4: Based on the structural equilibrium theory, Perron-Frobenius theorem, and matrix analysis method in graph theory, and combined with the block matrix structure after network reconstruction, the consensus formation conditions and convergence rules of the dual-viewpoint dynamics model are derived for two scenarios: heterogeneous networks with forgetful / non-forgetful individuals and homogeneous networks without forgetful individuals. The influence mechanism of different network topological characteristics (structural equilibrium / imbalance) and individual classification characteristics on the evolution of private and expressed viewpoints is clarified. At the same time, a rigorous mathematical judgment basis and quantitative analysis method for convergence are given.

[0077] For network reconstruction A non-forgetful individual, A heterogeneous network of forgetful individuals, with submatrices corresponding to each forgetful individual. Based on the structural balance, the consensus formation rules of private viewpoints and expressed viewpoints are derived in two scenarios, while the convergence characteristics of non-forgetful individuals are clarified.

[0078] when When the structure is unbalanced (e.g.) Figure 3 (as shown), and the time-varying influence matrix sequence To achieve consistent joint strong connectivity and pressure influence matrix partitioning and Having the same non-zero element distribution and satisfying the row stochastic property requirement: the private views and expressed views of forgetful individuals reach zero consistency, forming a neutral consensus; the two views of non-forgetful individuals converge to a unified stable value;

[0079] when When the structure is in equilibrium (e.g.) Figure 2 (as shown), and the time-varying influence matrix sequence To achieve consistent joint strong connectivity and pressure influence matrix partitioning and With the same non-zero element distribution, the private views and expressed views of forgetful individuals form a polarized consensus, that is, all forgetful individuals are eventually divided into two opposing groups. Views within the same group tend to be consistent, while views between different groups tend to be opposite, which is consistent with the network interaction logic of cooperation and confrontation mentioned above; the dual views of non-forgetful individuals converge to a unified stable value.

[0080] All individuals in the network are non-forgetful (including stubborn individuals and individuals influenced by stubborn individuals), and the time-varying influence matrix sequence... For consistent joint strong connectivity, pressure influence matrix and Having the same distribution of non-zero elements, and the initial viewpoint At the same time, it satisfies the requirement of row randomness, ensuring that the opinion values ​​of all individuals remain within the initial interval. Furthermore, the convergence process is exponential, exhibiting a relatively fast convergence speed, which aligns with the evolutionary characteristics of real-world social networks.

[0081] Example

[0082] Example 1: Including amnesiac individuals and Imbalanced networks (such as Figure 3 As shown in the figure, a social network was formed by selecting 8 individuals, including non-forgetful individuals. ( Forgetful individuals ( Time-varying influence matrix submatrix Set as structural imbalance, pressure influence matrix and They have the same distribution of non-zero elements. The initial viewpoint is from... Selected from a uniform distribution, with the initial values ​​of private viewpoints and expressed viewpoints being equal: , Numerical simulations show that the private and expressed viewpoints of forgetful individuals gradually converge to 0, while the dual viewpoints of non-forgetful individuals converge to 0. The stable values ​​within the interval verify the consensus formation pattern under structural imbalance, such as... Figure 4 and Figure 5As shown.

[0083] Example 2: Including amnesiac individuals and Network structure balance (e.g.) Figure 2 As shown), a social network was formed by selecting 8 individuals, including non-forgetful individuals. ( Forgetful individuals ( Time-varying influence matrix submatrix The pressure effect matrix is ​​set as shown. and They have the same distribution of non-zero elements. The initial viewpoint is from... Selected from a uniform distribution, with the initial values ​​of private viewpoints and expressed viewpoints being equal: , Numerical simulations show that forgetful individuals fall into two opposing groups: one group's viewpoint converges to approximately 0.2, while the other converges to approximately -0.2, resulting in polarization. For non-forgetful individuals, both viewpoints converge to a unified, stable value, consistent with the consensus characteristics of structural equilibrium. Figure 6 and Figure 7 As shown.

[0084] Example 3: A social network was formed by selecting 8 individuals, including those who are not forgetful. Time-varying influence matrix Satisfying consistent joint strong connectivity, pressure influence matrix and They have the same distribution of non-zero elements. The initial viewpoint is from... Selected from a uniform distribution, with the initial values ​​of private viewpoints and expressed viewpoints being equal: , Numerical simulations show that the private and expressed viewpoints of all individuals converge to the same stable value, such as... Figure 8 As shown.

Claims

1. A method for forming consensus in a dual-viewpoint network based on stubbornness and dynamic interaction, characterized in that, Includes the following steps: Step 1, Construct a time-varying influence network model: Use a signed directed graph to describe the interpersonal interactions and interdependencies among individuals in the social network, and define the time-varying influence matrix. The matrix represents trust relationships, where the positive and negative values ​​of the matrix elements correspond to cooperation and antagonism, and satisfy the properties of row randomness and strong connectivity. Step 2, establish a dual-viewpoint dynamics model: define an individual's private viewpoint and expressed viewpoint, where the private viewpoint is the individual's true internal viewpoint, and the expressed viewpoint is the external viewpoint that the individual transmits to neighboring individuals. Based on individual stubbornness and the resilience of group viewpoint pressure, establish viewpoint updating rules and the competitive and cooperative relationships between individuals. Step 3, Individual Classification and Network Reconstruction: Individuals in the network are classified into forgetful individuals and non-forgetful individuals. Forgetful individuals are neither stubborn nor affected by stubborn individuals, while non-forgetful individuals are either stubborn individuals or individuals affected by stubborn individuals. The time-varying influence matrix is ​​reconstructed based on this classification. Step 4, consensus formation and convergence determination: based on the reconstructed network structure, combined with matrix structural balance analysis.

2. The method for forming a dual-viewpoint network consensus based on stubbornness and dynamic interaction according to claim 1, characterized in that, Step 1 is described in detail as follows: Using a signed directed graph Describe social networks, in which For a set of individual nodes, Let be a set of directed edges. This is the edge weight matrix; edges Represents an individual For individuals There is an impact, and the weight is significant. Positive values ​​indicate cooperation, and negative values ​​indicate competition; Time-varying influence matrix Satisfying row-randomness and strong connectivity ensures efficient information transmission within the network; employing a boosting method to expand the dimensionality of the cooperative-competitive network; and adjusting the individual influence matrix. The breakdown is as follows: in, off-diagonal matrix Decomposed into in, and Each and the individual A set of neighboring individuals with cooperative relationships and individuals A set of neighboring individuals that are in competition with each other. For individuals in the evolution of private viewpoints Individual The influence weight.

3. The method for forming a dual-viewpoint network consensus based on stubbornness and dynamic interaction according to claim 2, characterized in that, Step 2 is described in detail below: Define individual Private viewpoint and expressing opinions Private viewpoints are the individual's true internal viewpoints, while expressed viewpoints are the external viewpoints that an individual conveys to their neighbors. Private viewpoint updates: Taking into account the private viewpoints of cooperating neighbors, the persistence of one's own initial viewpoint, and the impact of competing neighbors' expressed viewpoints, this is achieved through influence sensitivity. Modulate the intensity of neighborhood influence. It represents the degree to which an individual adheres to their initial viewpoint; Expression of updated viewpoints: formed based on individual private opinions and neighbor feedback, and strengthened by the pressure of group viewpoints. Balancing one's own private perspective with the influence of the group, The larger the value, the more inclined the individual is to insist on expressing their own views to the outside world; Therefore, the dual-viewpoint dynamic model is derived as follows: in, For individuals in the process of expressing viewpoints evolving Individual The influence weight.

4. The method for forming a dual-viewpoint network consensus based on stubbornness and dynamic interaction according to claim 3, characterized in that, Step 3 is as follows: When both non-forgetful and forgetful individuals exist in a two-viewpoint dynamics model, in a time-varying influence network... In the process, non-forgetful individuals and forgetful individuals are renumbered as follows: and Of these, the number of non-amnesiac individuals was... The number of forgetful individuals is ,Right now If all individuals are reordered according to the categories of non-forgetful and forgetful individuals, the diagonal matrix is ​​represented as: in, Based on the reordering of non-forgetful and forgetful individuals, the time-varying influence matrix Rewritten as: 。 5. The method for forming a dual-viewpoint network consensus based on stubbornness and dynamic interaction according to claim 4, characterized in that, Step 4 is as follows: When the network submatrix When the structure is unbalanced, the private opinions and expressed opinions of forgetful individuals reach zero consensus, while the private opinions and expressed opinions of non-forgetful individuals converge to a unified and stable value. When the network submatrix When the structure is in equilibrium, the private opinions and expressed opinions of forgetful individuals become polarized, while the private opinions and expressed opinions of non-forgetful individuals converge to a unified stable value. When there are no forgetful individuals in the network, all individuals' private opinions and expressed opinions converge to a uniform stable value.

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