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

  • D. Sadhukhan
  • B. Mondal
  • M. Maiti
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)


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.


Prey–predator Stability Reserved area Intratrophic predation Optimal harvesting 


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Haldia Government CollegeHaldia, Purba MidnaporeIndia
  2. 2.Raja N.L.K. Womens CollegeMidnaporeIndia
  3. 3.Department of Applied MathematicsVidyasagar UniversityMidnaporeIndia

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