Title: Bifurcation behaviour of a discrete differential algebraic prey – Predator system with Holling type II functional response and prey refuge
Abstract: The refuge of prey species is a biological factor necessary for the coexistence of the species and hence it is yet another factor of great interest due to defensive properties of the prey against the predation. We propose a class of discrete differential algebraic prey predator system with Holling Type II functional response and prey refuge. The system is found to possess trivial, semi-trivial and interior equilibrium states existing under certain conditions. Also we examine the existence and uniqueness of the solutions of the system. Dynamical behaviour of the system is investigated through linear stability analysis of the equilibrium states. Moreover, this system undergoes bifurcation when the chosen parameter passes through a critical value, and closed invariant curves arise from a stable equilibrium state. The analytical results are strengthened with appropriate numerical examples and they demonstrate chaotic behaviours over a wild range of parameters. The computation of maximal Lyapunov exponents confirms the existence of chaos. Finally chaos control is achieved by linear feedback control and hybrid control methods.
Publication Year: 2020
Publication Date: 2020-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 3
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