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Nonlinear Dynamics

, Volume 79, Issue 4, pp 2251–2270 | Cite as

Complex dynamics of ecological systems under nonlinear harvesting: Hopf bifurcation and Turing instability

  • Ranjit Kumar UpadhyayEmail author
  • Parimita Roy
  • Jyotiska Datta
Original Paper

Abstract

In this paper, we study the complex dynamics of a spatial nonlinear predator-prey system under harvesting. A modified Leslie–Gower model with Holling type IV functional response and nonlinear harvesting of prey is considered. We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. Numerical simulations were performed to figure out how Turing patterns evolve under nonlinear harvesting. Simulation study leads to a few interesting sequences of pattern formation, which may be relevant in real world situations.

Keywords

Turing instability Pattern formation Hopf bifurcation Harvesting Holling type IV functional response 

Notes

Acknowledgments

This work is supported by University Grants Commission, Govt. of India under grant no. F. No. 42-16/2013(SR) to the corresponding author (R. K. Upadhyay).

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Ranjit Kumar Upadhyay
    • 1
    Email author
  • Parimita Roy
    • 1
  • Jyotiska Datta
    • 2
  1. 1.Department of Applied MathematicsIndian School of MinesDhanbadIndia
  2. 2.Centre for MathematicsCentral University of OrissaKoraputIndia

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