Predator-prey fishery model under deterministic and stochastic environments: a mathematical perspective
type: Item
instance of: scholarly article
title: Predator-prey fishery model under deterministic and stochastic environments: a mathematical perspective
zbMATH Open document ID: 1258.34095
author: Swapan Chakraborty
author: Nandadulal Bairagi
author: Samares Pal
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2013-01-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6124748
zbMATH Keywords: predator-prey models
zbMATH Keywords: deterministic
zbMATH Keywords: stochastic
zbMATH Keywords: ratio-dependence
zbMATH Keywords: harvesting
zbMATH Keywords: dissipativeness
zbMATH Keywords: permanence
zbMATH Keywords: bistability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6124748