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Optimal harvesting and stability of a predator–prey model for fish populations with schooling behavior

Abstract

In this paper, the schooling behavior of prey fish population in a predator–prey interaction is investigated. By taking an economical interest which can be elaborated by the presence of nonselective harvesting into consideration, we studied the dynamical behavior. The existence, positivity and boundedness of solution have been established. The analysis of the equilibrium states is presented by studying the local and the global stability. The possible types of local bifurcation that the system can undergoes are discussed. The effect of fishing effort on the evolution of the species is examined. Further, by using Pontryagin’s maximum principle a proper management strategy has been used for avoiding the extinction of the considered species and maximizing the benefits. For the validation of the theoretical result, several of graphical representations have been used.

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Correspondence to Salih Djilali.

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Hacini, M.E.M., Hammoudi, D., Djilali, S. et al. Optimal harvesting and stability of a predator–prey model for fish populations with schooling behavior. Theory Biosci. 140, 225–239 (2021). https://doi.org/10.1007/s12064-021-00347-5

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  • DOI: https://doi.org/10.1007/s12064-021-00347-5

Keywords

  • Predator–prey model
  • Schooling behavior
  • Optimal harvesting
  • Global stability
  • Hopf bifurcation