ANZIAM J.
45 (2004), 443-456
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Harvesting in a two-prey one-predator fishery: a bioeconomic model
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T. K. Kar
Department of Mathematics
B.E. College (Deemed University)
Howrah 711103
India
tkar@math.becs.ac.in
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Abstract
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A multispecies harvesting model with
interference is proposed. The model is based on
Lotka-Volterra dynamics with two competing
species which are affected not only by
harvesting but also by the presence of a
predator, the third species. In order to
understand the dynamics of this complicated
system, we choose to model the simplest possible
predator response function in which the feeding
rate of the predator increases linearly with
prey density. We derive the conditions for global
stability of the system using a Lyapunov
function. The possibility of existence of a
bioeconomic equilibrium is discussed. The optimal
harvest policy is studied and the solution is
derived in the equilibrium case using
Pontryagin's maximal principle. Finally, some
numerical examples are discussed.
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