Abstract
A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin’s maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.
Highlights
IntroductionIntroducing red devil fish species in freshwater ecosystems has threatened the presence of commercial fish (such as, tilapia and goldfish) in the habitats
Introducing red devil fish species in freshwater ecosystems has threatened the presence of commercial fish in the habitats
We propose and analyze an ecological model of multispecies harvesting of two competing prey species and a predator species
Summary
Introducing red devil fish species in freshwater ecosystems has threatened the presence of commercial fish (such as, tilapia and goldfish) in the habitats. The combined harvesting of two competing species from the aspect of bionomic was studied and discussed for the optimal equilibrium policy [3,4,5,6,7]. Das et al [8] and Chaudhuri et al [9] proposed the model one prey – one predator with combined harvesting They analysed the dynamical behaviour of the model and the optimal harvesting policy. Rao et al [10] investigated analytically the dynamical behaviour of the model for three species with one prey and two competing predators They discussed the policy of optimal harvesting.
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