Title: Predator-prey fishery model under deterministic and stochastic environments: a mathematical perspective

Authors: Swapan Chakraborty; Samares Pal; Nandadulal Bairagi

Addresses: Baruipara High School, Halisahar, 24 Parganas (N), West Bengal, India. ' Department of Mathematics, University of Kalyani, Kalyani 741235, India. ' Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

Abstract: In this paper, we study a predator-prey fishery model with ratio-dependent functional response under deterministic and stochastic environments. Prey and predator populations are continuously harvested following the CPUE (catch-per-unit-effort) hypothesis. Mathematical results like positive invariance, dissipativeness, stability of equilibria and permanence of the system have been established. The dynamics of the zero equilibria have been thoroughly investigated to find out conditions under which trajectories starting from the domain of interest can reach the origin following any fixed direction. Computer simulations have been carried out to illustrate different analytical findings. Our results indicate that the system may exhibit different kinds of bistabilities depending on the harvesting effort and initial population densities. Investigation also reveals that exploited marine fish populations can exhibit steady, cyclic or irregular behaviour.

Keywords: predator-prey models; deterministic; stochastic; ratio-dependence functional response; harvesting; dissipativeness; permanence; bistability; fishery models; modelling; equilibria stability; marine fish populations.

DOI: 10.1504/IJDSDE.2012.049887

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.3, pp.215 - 241

Published online: 18 Oct 2012 *

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