Existence and Uniqueness of Asymptotic Periodic Solution in the Cyclic Four Species Predator- Prey Model

Document Type : Original Paper

Authors

Department of Mathematics, University of Neyshabur, Neyshabur, Iran

Abstract

In the past decades, in the area of mathematical ecology, the dynamical properties occurring in the predator-prey models have been studied. Moreover, the stability and boundedness of the solution for population model such as cyclic, delayed and etc. have been studied. In the present paper, a nonlinear cyclic predator-prey system with sigmoidal type functional response is analyzed. Indeed, a model of four species predator-prey system has been investigated and the sufficient conditions for stability and boundedness of the solutions of predator-prey system have been presented. For this purpose, the differential inequality theory is employed and finally, by constructing a suitable Lyapanov function the existence and uniqueness of asymptotically periodic solution which is globally asymptotically stable are proved.

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References

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Journal of Advanced Mathematical Modeling
Volume 9, Issue 1
March 2019
Pages 143-160

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History

  • Receive Date: 14 January 2018
  • Revise Date: 17 October 2018
  • Accept Date: 30 October 2018

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