Computational Ecology and Software (Jun 2019)
Bifurcation analysis and chaos control in a discrete-time predator-prey system with Crowley-Martin functional response
Abstract
In this paper, the dynamics of a discrete-time predator-prey system with Crowley-Martin functional response is examined. Via application of the center manifold theorem and bifurcation theorems, we algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R2+. Numerical simulations are presented not only to validate analytical results but also to reveal new dynamical behaviors which include bifurcations, phase portraits, period- 5, 6, 7, 10, 11, 15, 16, 17, 21, 28, and period- 51 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 chaotic behaviors of the system. Finally, we apply a strategy of feedback control to control chaos exists in the system.
