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.
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