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Prey–predator–scavenger model with Monod–Haldane type functional response

  • Prabir PanjaEmail author
Article
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Abstract

In this paper, we have developed a prey, predator and scavenger interaction dynamical model. The positivity, boundedness and stability conditions of our proposed system have been derived. Hopf bifurcation analysis has been done theoretically with respect to half saturation constant in the absence of direct measure of inhibitory effects \((\phi _1)\). Also, we have numerically studied Hopf bifurcation with respect to direct effects of inhibitory effects \((\phi _2)\) related to Monod–Haldane type functional response, carrying capacity of prey \((\gamma )\), death rate of scavenger \((\mu )\), conservation rate of prey \((\alpha )\) and harvesting rate of predator \((\eta )\). It is observed that the intra-species competition can lead our proposed system towards stability. It is also found that the harvesting of predator can control the chaotic dynamics of our proposed system. The increase of death rate of scavenger species can be stabilized our proposed system. Finally, some numerical simulation results have been presented for better understanding the dynamics of our proposed model.

Keywords

Prey Predator Scavenger Stability Hopf bifurcation 

Mathematics Subject Classification

92B05 37C75 37C25 

Notes

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied ScienceHaldia Institute of TechnologyPurba Medinipur, HaldiaIndia

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