%0 Journal Article
%T Chaos Induced by Snap-Back Repeller in a Two Species Competitive Model
%A Tahmineh Azizi
%A Bacim Alali
%J American Journal of Computational Mathematics
%P 311-328
%@ 2161-1211
%D 2020
%I Scientific Research Publishing
%R 10.4236/ajcm.2020.102017
%X In this paper, we investigate the complex dynamics of two-species Ricker-type discrete-time competitive model. We perform a local stability analysis for the fixed points and we will discuss about its persistence for boundary fixed points. This system inherits the dynamics of one-dimensional Ricker model such as cascade of period-doubling bifurcation, periodic windows and chaos. We explore the existence of chaos for the equilibrium points for a specific case of this system using Marotto theorem and proving the existence of snap-back repeller. We use several dynamical systems tools to demonstrate the qualitative behaviors of the system.
%K Complex Dynamics
%K Snap-Back Repeller
%K Marotto Theorem
%K Persistence Theory
%K Bifurcation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=101201