Research On Delayed Replicator Equation Based On Game Models

It is a research hotspot of game theory to study the evolution law of classical game models by using dynamical systems.The replicator equation is a mathematical model based on Darwin's evolutionary tenet.It is the most widely used differential equation in the field of evolutionary game research.Time delay is a common influencing factor in practical problems,so it is of great significance to study replicator equation with delay.In this paper,the standard rock-paper-scissors game and snowdrift game models are studied respectively.Firstly,based on the standard rock-paper-scissors game,the delay replicator equations with single mutation mechanism and global mutation are established respectively,and the influence of time delay in different models of mutation mechanism is analyzed,and the bifurcation critical value is derived.The study shows that the internal equilibrium point is stable when the time delay is less than the critical value,Hopf bifurcation occurs when the delay passes through the critical value,and the conclusion is verified by numerical simulation.Secondly,based on two-community game,the effects of discrete strategy and spatial delay on replicator dynamics are discussed.The stability conditions of neutral evolutionary stability strategy are derived,and the numerical simulation of the improved snowdrift game model is given to verify the correctness of the theoretical results,and the stability of the speed is compared.Finally,the effects of different spatial delays on the stability of the intermediate evolutionary stability strategy are analyzed,and the stability conditions are derived and verified by numerical simulation.