Authors: Jyotirmoy Roy; Shariful Alam
Addresses: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur B. Garden, Howrah – 711103, India ' Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur B. Garden, Howrah – 711103, India
Abstract: In this paper, a generalised prey-predator system has been analysed, where the whole habitat is divided into free zone and reserved zone. Only prey species can access the reserved zone where predation is strictly prohibited, whereas in the free zone both the species can cohabit and naturally predation is allowed. The migration rates of the prey species from reserved zone to unreserved zone and vice-versa both depends on predator's availability. The stability analysis of the model system has been performed in a systematic manner and system persistence criterion has been established. Hopf bifurcation occurs when the prey migration rate from reserved zone to unreserved zone crosses a certain threshold value. It is also found that the prey migration rate has stabilising effect on the dynamics of the system. Finally numerical simulation has been carried out to support our analytical findings.
Keywords: prey-predator model; reserved zone; stability and persistence; Hopf bifurcation; limit cycle.
International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.5, pp.383 - 400
Received: 01 Jul 2018
Accepted: 02 Feb 2019
Published online: 30 Nov 2020 *