Modeling And Analysis Of Coopetitive Social Networks In Opinion Dynamics

In the society,the relationships between individuals are not only cooperation,but also competition.Therefore,it is of great significance to study the opinion dynamics based on coopetitive social networks.In order to study the evolution of opinion values in different scenarios,this thesis combines leader-follower mechanism,multiplicative noise,and time delay with the Altafini model respectively to establish new opinion dynamics models and analyze the stability.Due to the existence of the leader,the leader-follower mechanism is introduced to model the social network with the leader.The effects of the static leader and the dynamics leader are studied respectively.Consider the subjective initiative in decision-making of individuals,this thesis simulates subjective by adding multiplicative noise,and explores the evolution of individual opinion value under the effect of multiplicative noise.For the time delay of information transmission between individuals,this thesis introduces the time delay on the basis of the system adding multiplicative noise,and analyzes the stability of the whole system.The main work and research results of this thesis are as follows:(1)Based on the Altafini model,leader-follower mechanism is introduced to establish a new opinion dynamics model under the coopetitive network,and the effects of the static leader and the dynamic leader on the opinion values of followers are studied by using matrix theory and Laplace frame.The necessary and sufficient conditions for the followers’opinion value converge to the leader’s value or its opposite are proposed when the leader’s opinion value is static.When the leader’s opinion value is dynamic,if the leader’s opinion value changes at a constant rate,the difference between the follower’s opinion value and the leader’s opinion value converges to a constant under certain conditions.(2)Considering that the agents in society are affected by irrelevant information and influenced by subjective initiative in decision-making,a new stochastic opinion dynamics model was established by adding multiplicative noise to Atafini model,and the evolution of opinions values under the influence of multiplicative noise was explored.A sufficient condition is established which ensure the equilibrium point of the system is almost sure exponential stable.When the the noise intensity and topological structure meet certain conditions,all the agents’ opinion values will converge to 0.(3)A stochastic Atafini model with multiplicative noise and time delay is established.We get the conservative boundary of noise intensity and time delay is obtained,which can make the opinion dynamic system affected by both multiplicative noise and time delay almost sure exponential stable by using the stochastic Lyapunov method.