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Wu, D.Y. and Zhang, H. (2014) Bifurcation Analysis of a Two-Species Competitive Discrete Model of Plankton Allelopathy. Advances in Difference Equations, 2014, Article No.: 70.
https://doi.org/10.1186/1687-1847-2014-70

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.