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DYNAMICS OF A MODIFIED HOLLING-TANNER PREDATOR-PREY MODEL WITH DIFFUSION

  • SAMBATH, M. (DEPARTMENT OF MATHEMATICS, PERIYAR UNIVERSITY) ;
  • BALACHANDRAN, K. (DEPARTMENT OF MATHEMATICS, BHARATHIAR UNIVERSITY) ;
  • JUNG, IL HYO (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
  • Received : 2018.12.29
  • Accepted : 2019.06.18
  • Published : 2019.06.25

Abstract

In this paper, we study the asymptotic behavior and Hopf bifurcation of the modified Holling-Tanner models for the predator-prey interactions in the absence of diffusion. Further the direction of Hopf bifurcation and stability of bifurcating periodic solutions are investigated. Diffusion driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally we illustrate the theoretical results with some numerical examples.

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