Bifurcation and stability analysis of a ratio-dependent predator-prey model with predator harvesting rate

Z. Lajmiri, R. Khoshsiar Ghaziani and Iman Orak

Chaos, Solitons & Fractals, 2018, vol. 106, issue C, 193-200

Abstract: In this paper, we study the bifurcation and stability of a ratio-dependent predator-prey model with nonconstant predator harvesting rate. The analysis is carried out both analytically and numerically. We determine stability and dynamical behaviours of the equilibria of this system and characterize codimension 1 and codimension 2 bifurcations of the system analytically. Our bifurcation analysis indicates that the system exhibits numerous types of bifurcation phenomena, including Fold, Hopf, Cusp, and Bogdanov–Takens bifurcations. We use the numerical software MATCONT, to compute curves of equilibria and to compute several bifurcation curves. We especially approximate a family of limit cycles emanating from a Hopf point. Our results generalize and improve some known results and show that the model has more rich dynamics than the ratio-dependent predator-prey model without harvesting rate.

Keywords: Hopf bifurcation; Bogdanov-Takens bifurcation; Cusp bifurcation; Dynamical behavior; Limit cycle (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:106:y:2018:i:c:p:193-200

DOI: 10.1016/j.chaos.2017.10.023

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