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International Journal of Dynamics and Control

, Volume 7, Issue 4, pp 1321–1349 | Cite as

Influence of dispersal and strong Allee effect on a two-patch predator–prey model

  • Sangeeta SahaEmail author
  • G. P. Samanta
Article

Abstract

This work aims to study a population-dispersal dynamics for predator–prey interactions in a two patch environment with strong Allee effect among prey species in both patches. It is assumed that the prey species are movable and their dispersal between patches is directed from lower fitness to the higher fitness patch (exhibiting balanced dispersal). Existence and stability criterion of the interior equilibrium point of the system is analyzed in presence as well as in absence of dispersal speed. It has been observed that Allee threshold takes an important role to destabilize the system while the prey individuals evolve in their own patches independently. Moreover dispersal cannot destabilize populations at the interior equilibrium, i.e., if a predator–prey equilibrium without dispersal is in stable state then this situation cannot be destabilized when prey species move between two patches. Numerical simulations using MATLAB validate the analytical results. The occurrence of transcritical as well as Hopf bifurcation has also been reported.

Keywords

Allee effect Dispersal Balanced dispersal Stability Trophic cascade Bifurcation 

Notes

Acknowledgements

The authors are grateful to the anonymous referees and Editor in Chief Prof. Jian-Qiao Sun for their careful reading, valuable comments and helpful suggestions, which have helped to improve the presentation of the work significantly. The authors are also grateful to Prof. Vlastimil Krivan, Department of Mathematics and Biomathematics at Faculty of Science, University of South Bohemia, Czech Republic for his help and encouragement. Part of this work was done by G. P. Samanta during his visit in January 2017 at the University of South Bohemia, Czech Republic. G. P. Samanta is thankful to Indian Institute of Engineering Science and Technology, Shibpur, India for financial support for this academic visit through CPDA. The first author (Sangeeta Saha) is thankful to the University Grants Commission, India for providing JRF.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia

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