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Computational Ecology and Software, 2019, 9(2): 37-57
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Article

Bifurcation analysis and chaos control in a discrete-time predator-prey system with Crowley-Martin functional response

S. M. Sohel Rana
University of Dhaka, Dhaka-1000, Bangladesh

Received 29 December 2018;Accepted 5 February 2019;Published 1 June 2019
IAEES

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.

Keywords predator-prey system with Crowley-Martin functional response;bifurcations;chaos;Lyapunov exponents;feedback control.

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