BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE-TIME PREDATOR-PREY SYSTEM OF LESLIE TYPE

We investigate the dynamics of a discrete-time predator-prey system of Leslie type. We show algebraically that the system passes through a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+ using center manifold theorem and bifurcation theory. Numerical simulations are implimented not only to validate theoretical analysis but also exhibits chaotic behaviors, including phase portraits, period-11 orbits, invariant closed circle, and attracting chaotic sets. Furthermore, we compute Lyapunov exponents and fractal dimension numerically to justify the chaotic behaviors of the system. Finally, a state feedback control method is applied to stabilize the chaotic orbits at an unstable fixed point.

• Publication year

  2019

• Venue

  The Journal of Applied Analysis and Computation

• Publication date

  Unknown publication date

• Fields of study

  Mathematics

• Identifiers
  DOI 10.11948/2019.31
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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