Dynamic Coupling Studies Of Cooperative Behavior And Synchronization On Complex Networks

Synchronous and cooperative behaviors are widespread in economic,social and theoretical research.Many scholars have studied synchronous and cooperative behaviors separately,but few have combined them.In fact,in real life,there is a coupling relationship between cooperation and synchronization due to the cost of interaction between individuals.Therefore,aiming at the coupling relationship between cooperation and synchronization,based on the Kuramoto model,this thesis establishes a model that contains synchronization and cooperation that is more in line with the practical significance.At the same time,the optimal selection method is used to observe and explore the changes of cooperation rate and synchronization rate under different optimal selection parameters.Based on the ER network,this thesis introduces cost and benefit into the classic Kuramoto model,thus combining synchronization and cooperation.Different from the past,the oscillator needs to pay the cost to synchronize with the neighbor,such synchronization behavior can be understood as cooperation in this thesis,while the remaining oscillator unwilling to pay the cost will wait for the partner to synchronize to their phase,namely free rider,such synchronization behavior can be understood as defection in this thesis.Secondly,different from previous studies,this thesis adopts the optimal selection method when selecting neighbors for learning strategies,that is,among individuals interacting with themselves,the neighbors with higher payoff are more likely to be selected as contributors to the strategies.Specifically,in this thesis,the traditional random selection and optimal selection methods are firstly compared,and it is found that the optimal selection has a good promoting effect on the maintenance of cooperative and synchronous behavior.Then,this thesis studies the cooperation and synchronization rate under different average degrees.The results show that with the increase of the average degree,the cooperation rate first gradually increases,then stabilizes at a high level,and finally gradually decays to close to 0.And the smaller the relative cost and coupling strength of the system,the larger the range of average degree of cooperation can be maintained.However,the evolution trend of synchronization rate is similar to that of cooperation rate.The difference is that there is an optimal average degree of synchronization rate,that is,the synchronization rate of the system is the highest.Finally,this thesis studies the influence of optimal selection parameters on cooperation and synchronization behavior,and the results show that the variation trend of cooperation rate and synchronization rate is consistent.Secondly,when the optimal selection parameter is positive and large,each individual will choose the neighbor with higher payoff for learning in the interaction with the neighbor with a greater probability;on the contrary,when the optimal selection parameter is negative,the individual will choose the neighbor with lower payoff for learning in the interaction with the neighbor with a greater probability,that is,the optimal selection is actually the selection of payoff.Finally,this study is helpful to deepen the research on the dynamic coupling of cooperation and synchronization behavior on complex networks,providing a theoretical basis for the evolution of optimal selection conducive to cooperation and synchronization behavior,and enriching the research on cooperative behavior in the Kuramoto model.