Controlling Chaos of the Ricker Population Model by OGY Method

Guo Feng

doi:10.3844/ajbbsp.2020.424.431

Abstract

The chaotic dynamics of the Ricker mapping are studied. Controlling chaos of the Ricker population model is searched by OGY control method. The dynamic behavior in the Ricker mapping is very complex in different values of a. When the value of a is changed from 0.455 to 90, the mapping goes through doubling bifurcation to Neimark-Sacker bifurcation. Several strange attractors coexist at last. Through the numerical simulation and analysis of the bifurcation and phase diagrams of the mapping, it is consistent with the theoretical analysis. Studies have shown that ecological balance can be achieved by appropriately adjusting the birth rate a, survival rate b.

Highlights

The Leslie model (Caswell, 2001) is an individual population model mainly used for key age structures of demographics and the conservation ecology.Following ecologists’ discoveries and in order to help ecologists model this kind of groups, ubiquitous age structure begins an extension study of the Leslie population model. in which the specific probability of survival and reproduction depends on population density
Through the numerical simulation and analysis of the bifurcation and phase diagrams of the mapping, it is consistent with the theoretical analysis
It controls the chaotic control of Ricker mapping, selects the amount of perturbation of the control parameter as the pole construction method by linear control theory

Summary

Introduction

The Leslie model (Caswell, 2001) is an individual population model mainly used for key age structures of demographics and the conservation ecology.Following ecologists’ discoveries and in order to help ecologists model this kind of groups, ubiquitous age structure begins an extension study of the Leslie population model. in which the specific probability of survival and reproduction depends on population density. Ugarcovici and Weiss (2007) proved that for some parameter regions, the strange attractor of Ricker model has an unique physical probability measurements. Research on chaos control of 2-D of shock vibration system based on OGY method (Feng et al, 2018). Romeiras et al (1992) through the use of polling mapping technology in system control, the OGY method has been further improved.

Results

Conclusion