Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment

Author(s)
Mellachervu Naga Srinivas,
Mantripragada Ananata Satya Srinivas,
Kalyan Das,
Nurul Huda Gazi

Abstract

In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.

In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system with stage structure in an aquatic environment that consists of two zones namely unreserved zone (fishing permitted) and reserved zone (fishing is strictly prohibited). In this model we introduce a stage structure in which predators are split into two kinds as immature predators and mature predators. It is assumed that immature predators cannot catch the prey and their foods are given by their parents (mature predators). It is also assumed that the fishing of immature predators prohibited in the unreserved zone and predator species are not allowed to enter inside the reserved zone. The local and global stability analysis has been specified. Biological and Bionomical equilibriums of the system are derived. Mathematical formulation of the optimal harvesting policy is given and its solution is derived in the equilibrium case by using Pontryagin’s maximum principle.

Keywords

Prey Predator, Stage Structure, Local and Global Stability, Bionomic Equilibrium, Optimal Harvesting, Pontryagin’s Maximum Principle

Prey Predator, Stage Structure, Local and Global Stability, Bionomic Equilibrium, Optimal Harvesting, Pontryagin’s Maximum Principle

Cite this paper

nullM. Srinivas, M. Srinivas, K. Das and N. Gazi, "Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment,"*Applied Mathematics*, Vol. 2 No. 11, 2011, pp. 1405-1416. doi: 10.4236/am.2011.211199.

nullM. Srinivas, M. Srinivas, K. Das and N. Gazi, "Prey Predator Fishery Model with Stage Structure in Two Patchy Marine Aquatic Environment,"

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