Abstract
The model is based on Lotka-Volterra dynamics with two competing fish species which are affected not only by harvesting but also by the presence of a predator, the third species. The prey populations are taken as equally dominating populations so that the coefficients of their interspecific competition are taken equal. The conditions of local and global stability of the model and the possibility of bioeconomic equilibrium are derived. Some numerical simulations are also done at the end of the paper. The asymptotic stability and global stability corresponding to the numerical examples are graphically shown.
Highlights
The fishery management system consists of the interaction between the fish species and humans, and not just the fish population dynamics
The response of fish stock to human activities and the economic consequences of specific harvest strategies can be examined by including the management objectives in the models on which management decisions are based
In recent past numerous works on bioeconomic modeling and optimal harvesting of biological resources have been published in leading journals
Summary
The fishery management system consists of the interaction between the fish species and humans, and not just the fish population dynamics. The bioeconomic approach in fishery models combines fish population dynamics and the economic components of the fishery system. Hanneson (1993) applied the fishery bioeconomic model approach to identify economically optimal harvest strategies for the fishery for Arcto-Norwegian Cod, a species that exhibits considerable fluctuation in stock size. Because the market demand is price sensitive, fluctuating harvests will cause fluctuations This may stabilize or destabilize fishing revenue, depending upon whether price elasticity of ISSN 1913-1844 E-ISSN 1913-1852 www.ccsenet.org/mas. Bioeconomic exploitation of both the species in a Lotka-Volterra prey predator system was discussed by Chaudhuri and Saha Ray (1991), Krishna et al (1998) discussed the conservation of an exploited ecosystem with optimal taxation on harvesting, and Pradhan and Chaudhuri (1999) developed a two species model with taxation as a control instrument.
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