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Journal of Dynamical and Control Systems

, Volume 21, Issue 4, pp 605–624 | Cite as

A Study of Chaotic Dynamics and Its Possible Control in a Predator-Prey Model with Disease in the Predator

  • Krishna pada DasEmail author
Article

Abstract

The effect of parasites and pathogens in the prey population received a lot of attention, but disease in the predator population has been studied comparatively little in literature. In this study, we have considered a predator-prey model with disease in the predator population. Here, we have analyzed the local stability of the model system around the equilibria. We have derived the ecological as well as the disease basic reproduction numbers and analyzed the community structure of the model system by these numbers. Our numerical results reveal that disease introduction in the predator population produces chaotic dynamics. We have observed stable focus, limit cycles, period doubling, and chaos for variation of the force of infection in the predator population. It is also observed that half-saturation constants are responsible for occurrence and control of chaos. It is found that chaos may be prevented by increasing the predation efficiency of the infected predator.

Keywords

Disease in predator Chaos Stable Hopf bifurcation Reproduction number Half-saturation constant 

Mathematics Subject Classification (2010)

37N25 

Notes

Acknowledgments

The authors are grateful to the reviewers for their helpful comments and suggestions. The authors are also grateful to the editor for his suggestions.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Mahadevananda MahavidyalayaKolkataIndia

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