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Ricerche di Matematica

, Volume 68, Issue 2, pp 435–452 | Cite as

Asymptotic stability of one prey and two predators model with two functional responses

  • Harsha KharbandaEmail author
  • Sachin Kumar
Article
  • 103 Downloads

Abstract

We formulate a mathematical model to study the complex dynamical behavior of a three dimensional model consisting of one prey and two predators involving Beddington–DeAngelis and Crowley–Martin functional responses. The existence and stability conditions of the equilibrium points are analyzed. The global asymptotic stability of the interior equilibrium point, if exists, is proved by considering Lyapunov function. Several numerical simulations are performed to illustrate the theoretical analysis. The multiple states of stability are observed in one example whereas another example exhibits the global stability of interior equilibrium point.

Keywords

Prey–predator model Functional response Equilibrium points Stability Lyapunov function 

Mathematics Subject Classification

Primary 92D40 Secondary 34D20 49K15 70K05 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their extensive comments on the revision of the manuscript which really improved the quality of the paper. This research work is supported by University Grant Commission (UGC), Government of India to the author, Harsha Kharbanda (Sr. No. 2121440663).

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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of DelhiNew DelhiIndia

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