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Computational Ecology and Software, 2020, 10(4): 200-216
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Article

Dynamic complexity in a discrete-time predator-prey system with Holling type I functional response: Gompertz growth of prey population

Sarker Md. Sohel Rana
University of Dhaka, Dhaka 1000, Bangladesh

Received 16 March 2020;Accepted 25 April 2020;Published 1 December 2020
IAEES

Abstract
We consider a discrete-time predator-prey system with Holling type I functional response and Gompertz growth of prey population to study its dynamic behaviors. We algebraically show that the predator-prey system undergoes a flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB) in the interior of R²₊ when one of the model parameter crosses its threshold value. We determine the existence conditions and direction of bifurcations by using the center manifold theorem and bifurcation theorems. We present numerical simulations to illustrate theoretical results which include the bifurcation diagrams, phase portraits, appearing or disappearing closed curves, periodic orbits, and attracting chaotic sets. In order to justify the existence of chaos in the system, maximum Lyapunov exponents (MLEs) and fractal dimension (FD) are computed numerically. Finally, chaotic trajectories have been controlled by applying feedback control method.

Keywords predator-prey system;Gompertz growth;bifurcations;Lyapunov exponents;feedback control.

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