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Global Dynamics in a Beddington–DeAngelis Prey–Predator Model with Density Dependent Death Rate of Predator

  • Koushik Garain
  • Udai Kumar
  • Partha Sarathi MandalEmail author
Original Research
  • 75 Downloads

Abstract

The article aims to investigate a prey–predator model which includes density dependent death rate for predators and Beddington–DeAangelis type functional response. We observe the changes in the existence and stability of the equilibrium points and investigate the complete global dynamics of the model. A two-parametric bifurcation diagram has been described here which shows the effect of density dependent death rate parameter of predator. We have also examined all possible local and global bifurcations that the system could go through, namely transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, cusp bifurcation, Bogdanov–Takens bifurcation, Bautin bifurcation and homoclinic bifurcation.

Keywords

Predator–prey model Beddington–DeAngelis Functional response Stability analysis Bifurcation Global dynamics 

Notes

Acknowledgements

Koushik Garain and Partha Sarathi Mandal’s research are supported by SERB, DST project [Grant: YSS/2015/001548]. Udai Kumar is supported by research fellowship from MHRD, Government of India.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  • Koushik Garain
    • 1
  • Udai Kumar
    • 1
  • Partha Sarathi Mandal
    • 1
    Email author
  1. 1.Department of MathematicsNIT PatnaPatnaIndia

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