Analyzing Predator-Prey Interaction in Chaotic and Bifurcating Environments

Authors : Ansar Abbas, Abdul Khaliq

Pages : 207-218

Doi:10.51537/chaos.1357543

View : 170 | Download : 201

Publication Date : 2023-11-30

Article Type : Research Paper

Abstract :An analysis of discrete-time predator-prey systems is presented in this paper by determining the minimum amount of prey consumed before predators reproduce, as well as by analyzing the system\'s stability and bifurcation. In order to investigate the local stability of the interior equilibrium point of the proposed model, discrete dynamics system theory is employed first. Moreover, the characteristic equation is analyzed to determine the Neimark-Sacker bifurcation of the system. The normal form and bifurcation theory are used to investigate the NS bifurcation around the interior equilibrium point. Based on its analysis, the system exhibits Neimark-Sacker bifurcation when positive parameters are present and non-negative conditions are met. Develop a feedback control strategy to discover the region of stability of the chaotic behavior. By utilizing the maximum laypanuou exponent, the effect of initial conditions on developed systems is further explored. Finally, a computer simulation illustrates the results of the analysis.
Keywords : Lotka volterra stability, Predator Prey model fixed points, Neimark sacker bifurcation, Maximum lyapunov exponent, Chaos control