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Incorporating prey refuge in a prey-predator model with a Holling type I functional response: random dynamics and
Amalia Gkana1, Loukas Zachilas
1Department of Economics, University of Thessaly, 43 Korai str., 38333 Volos, Greece.
Abstract:
A prey-predator discrete-time model with a Holling type I functional response is investigated by incorporating a prey refuge. It is shown that a refuge does not always stabilize prey-predator interactions. A prey refuge in some cases produces even more chaotic, random-like dynamics than without a refuge and prey population outbreaks appear. Stability analysis was performed in order to investigate the local stability of fixed points as well as the several local bifurcations they undergo. Numerical simulations such as parametric basins of attraction, bifurcation diagrams, phase plots and largest Lyapunov exponent diagrams are executed in order to illustrate the complex dynamical behavior of the system.
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