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Bio-economic Prey–Predator Fishery Model with Intratrophic Predation, Time Delay in Reserved and Unreserved Area

  • 2018
  • OriginalPaper
  • Chapter
Published in:
Authors
D. Sadhukhan
B. Mondal
M. Maiti
Published in
Operations Research and Optimization
Publisher
Springer Singapore

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Abstract

In this paper, we have studied the dynamics of a fishery system by dividing the marine aquatic environment in two zones, one is free fishing zone where harvesting and predation are allowed and other is reserve zone which is used only for growing the small fishes to make the marine ecosystem stable. Here harvesting and predation are not allowed. In harvesting zone, there are predators which follow intratrophic predation. We also incorporate time delay in this intratrophic interaction. At the first part of the problem, we have studied the local stability and bionomic equilibrium of the system without time delay, and in the second part of the study, the stability and bifurcation of the model have been discussed taking delay parameter into account. Optimal harvesting policy with Pontrygian’s maximal principle has also been discussed for the model. Finally, some numerical results and simulation are given to illustrate the model.

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Title
Bio-economic Prey–Predator Fishery Model with Intratrophic Predation, Time Delay in Reserved and Unreserved Area
Authors
D. Sadhukhan
B. Mondal
M. Maiti
Copyright Year
2018
Publisher
Springer Singapore
Book
Operations Research and Optimization

Print ISBN: 978-981-10-7813-2

Electronic ISBN: 978-981-10-7814-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-981-10-7814-9_17
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