Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A MATHEMATICAL MODEL OF A PREY-PREDATOR TYPE FISHERY IN THE PRESENCE OF TOXICITY WITH FUZZY OPTIMAL HARVESTING

  • PAL, D. (Chandrahati Dilip Kumar High School (H.S.)) ;
  • MAHAPATRA, G.S. (Department of Mathematics, National Institute of Technology Puducherry) ;
  • MAHATO, S.K. (Department of Mathematics, Sidho-Kanho-Birsha University) ;
  • SAMANTA, G.P. (Department of Mathematics, Indian Institute of Engineering Science and Technology)
  • Received : 2019.07.20
  • Accepted : 2019.12.11
  • Published : 2020.01.30
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Abstract

In this paper, we have presented a multispecies prey-predator harvesting system based on Lotka-Voltera model with two competing species which are affected not only by harvesting but also by the presence of a predator, the third species. We also assume that the two competing fish species releases a toxic substance to each other. We derive the condition for global stability of the system using a suitable Lyapunov function. The possibility of existence of bionomic equilibrium is considered. The optimal harvest policy is studied and the solution is derived under imprecise inflation in fuzzy environment using Pontryagin's maximal principle. Finally some numerical examples are discussed to illustrate the model.

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References

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