Complex dynamics of a discrete-time predator-prey system with Holling IV functional response

Qianqian Cui, Qiang Zhang, Zhipeng Qiu and Zengyun Hu

Chaos, Solitons & Fractals, 2016, vol. 87, issue C, 158-171

Abstract: In this paper, a discrete-time predator-prey system with Holling-IV functional response is studied. We first classify the existence of the fixed points of the system, and further investigate their local stabilities. Then the local bifurcation theory for maps is applied to explore the variety of dynamics of the system. Sufficient conditions for the flip bifurcation and Neimark–Sacker bifurcation are provided. Numerical results demonstrate that the system may have more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behavior. The maximum Lyapunov exponent and sensitivity analysis also confirm the chaotic dynamical behaviors of the system.

Keywords: Predator-prey system; Discrete-time dynamical system; Chaos; Flip bifurcation; Neimark-Sacker bifurcation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:87:y:2016:i:c:p:158-171

DOI: 10.1016/j.chaos.2016.04.002

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