Chaotic dynamics and control in a discrete-time predator-prey system with Ivlev functional response

Abstract

In this paper, a discrete-time predator-prey system with a functional response of Ivlev type is examined to reveal its chaotic dynamics. We algebraically show that the system undergoes a flip bifurcation and/or Neimark-Sacker (NS) bifurcation in the interior of R2+ when one ofthe model parameter crosses its threshold value. Via application of the center manifold theorem and bifurcation theorems, we determine the existence conditions and direction of bifurcations. Numerical simulations are employed to validate analytical results which include bifurcations, phase portraits, periodic orbits, invariant closed cycle, sudden disappearance of chaotic dynamics and abrupt emergence of chaos, and attracting chaotic sets. Furthermore, maximum Lyapunov exponents and fractal dimension are computed numerically to justify the existence of chaos in the system. Finally, we apply a strategy of feedback control to control chaotic trajectories exist in the system.

Keywords

• predator-prey system with ivlev functional response
• bifurcations
• chaos
• lyapunov exponents
• feedback control