Refugia and Allee Effect in Prey Species Stabilize Chaos in a Tri-Trophic Food Chain Model

  • Binayak Nath
  • Nitu Kumari
  • Vikas Kumar
  • Krishna Pada DasEmail author
Original Research


In this paper a mathematical model is proposed and analyzed to study the dynamics of tri-trophic food chain model with refugia and allee effect in prey species. Criteria for local stability, instability and global stability of the non-negative equlibria are obtained. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system and global stability of the positive interior equilibrium solution are discussed. Further we pay attention to the chaotic dynamics which is produced by half-saturation constant. Our numerical simulations reveal that the three species food chain model without refugia and allee effect induced chaos from stable focus for increasing the value of half-saturation constant. We conclude that chaotic dynamics can be controlled by the Allee and refugia parameters.


Tri-trophic food chain Local stability Global stability Hopf bifurcation Direction of Hopf bifurcation Permanence and non-permanence 



The authors are grateful to the Editor and reviewers for their helpful comments and suggestions.


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2019

Authors and Affiliations

  • Binayak Nath
    • 3
  • Nitu Kumari
    • 2
  • Vikas Kumar
    • 2
  • Krishna Pada Das
    • 1
    Email author
  1. 1.Mahadevananda Mahavidyalaya MoniramporeKolkataIndia
  2. 2.School of Basic SciencesIndian Institute of Technology MandiMandiIndia
  3. 3.Department of PhysicsMahadevananda Mahavidyalaya MoniramporeKolkataIndia

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