An Application Of Coloured Noise In Spatial Evolutionary Game

The living environment of biont, which can be described by coloured noise, is constantly changing. Coloured noise has been a successful framework to discuss lots of issues in population dynamics, as the changes of environment should be considered in some population dynamics models. Based on the spatial evolutionary game model, this paper introduces the coloured noise, and discusses the effects of the colored noise on cooperation ratio when the system is stable.The first chapter not only introduces some types of colored noise, but also summarizes some methods which are used in generating colored noise and the applications of coloured noise in population dynamics. The second chapter presents spatial evolutionary game model and Monte Carlo Simulation method. Additionally, the spatial evolutionary game model with Von Neumann neighbours is analysed in the second chapter.The third chapter, which is the innovative part of this paper, introduces the spatial evolutionary game model with coloured noise and studies the changes of cooperation ratio by Monte Carlo Simulation method. Firstly, it introduces a spatial evolutionary game model in which the numbers of the individual's neighbors are different. Then we introduce another spatial evolutionary game model in which the population is constrained. We find that properly decreasing the population can increase cooperation ratio. At the last, we introduce the spatial evolutionary game model with coloured noise based on previous models. Our results reveal that the effect of coloured noise on cooperation ratio is related to the parameters of the game. That is to say, the coloured noise tends to increase cooperation ratio with low temptation of defection and it tends to decrease cooperation ratio with high temptation of defection. In fact, these models are the combination of coloured noise and spatial evolutionary game model.