The Study Of Dynamical Models About The Evolution Of Cooperation In Populations Which Are Not Well-mixed

There is full of competition and cruel slaughter around the natural world.Charles Darwin explained it as "struggle for existence",but there are also warm scenes that we often see even in the most evil predators,for example "parental care".Most of us would like to think that everyone is struggling for the sustainance and prevalence of his genes,that is to say,they are selfish.However,there is also exceptance in nature,the explanation about cooperation or altruism is widely divided and puzzling.Because it is clear that living beings are selfish according to our general understanding to the biological nature,cooperators are inclined to be invaded and excluded by defectors.This paper mainly discusses a mechanism for the evolution of cooperation in populations of the same species where interactions between individuals are not uniform. This includes two aspects:First of all,we introduce a uniform interaction rate which is interaction probability between individuals in unlimited populations.We find changes in interaction rates have a significant impact on evolutionary dynamics, and the evolution of cooperation seems not be difficult in these situations.When the ratio between the interaction rate of individuals that using cooperation play themselves and that of individuals that using cooperation play with the other type is large,cooperators can success in the evolution,and theoretically,they can coexist with defectors;When the ratio between the interaction rate of individuals that using defection play themselves and that of individuals using defection play with the other type is large,as long as the rate of cooperators in populations exceeds a certain value,they will exclude defectors.Secondly,we suppose the individuals of a finite population have control over the frequency and duration of interactions and they differ in the rate at which they seek new interactions.These differences have changed the payoff matrix in our model and thus,the result of evolution,cooperation has an opportunity to success.