Complex bifurcation patterns in a discrete predator–prey model with periodic environmental modulation

Pramana: Journal of physics

K P HARIKRISHNAN^1¹ 

[1] Department of Physics, The Cochin College, Cochin 682 002, India^1

关键词: Predator–prey model;    bifurcation patterns;    environmental modulation;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We consider the simplest model in the family of discrete predator–prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rateof the predator.We show that with the introduction of environmental modulation, the bifurcation structure becomes much more complex with bubble structure and inverse period doubling bifurcation. The model also displays the peculiar phenomenon of coexistence of multiple limit cycles in the domain of attraction for a given parameter value that combine and finally gets transformed into a single strange attractor as the control parameter is increased. To identify the chaotic regime in the parameter plane of the model, we apply the recently proposed scheme based onthe correlation dimension analysis. We show that the environmental modulation is more favourable for the stable coexistence of the predator and the prey as the regions of fixed point and limit cycle in the parameter plane increase at the expense of chaotic domain.

【 授权许可】

CC BY