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Guckenheimer, J. and Holmes, P. (1984) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Journal of Applied Mechanics, 51, 947.
https://doi.org/10.1115/1.3167759

has been cited by the following article:

• TITLE: Chaos Induced by Snap-Back Repeller in a Two Species Competitive Model

  AUTHORS: Tahmineh Azizi, Bacim Alali

  KEYWORDS: Complex Dynamics, Snap-Back Repeller, Marotto Theorem, Persistence Theory, Bifurcation

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.10 No.2, June 30, 2020

  ABSTRACT: 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.