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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Alternative Resource and Harvesting in Predator-prey Dynamics: Analyzing a Delay Model

Journal of Applied Nonlinear Dynamics 11(4) (2022) 927--948 | DOI:10.5890/JAND.2022.12.011

Sukumar Samanta$^{1}$, Banshidhar Sahoo$^2$, Pralay Poria$^3$, Sanat Kumar Mahato$^1$

$^{1}$ Department of Applied Mathematics, S.K.B. University, Purulia, West Bengal, India

$^2$ Department of Mathematics, Hiralal Bhakat College, Birbhum, West Bengal, India

$^3$ Department of Mathematics, Sabang Sajanikanta Mahavidyalaya, Paschim Medinipur, West Bengal, India

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Abstract

We study the effect of harvesting on the stability of a predator-prey system. Alternative resource is provided to predator population to reduce extinction probability of predator. The model is extended incorporating gestation time delay of predator as the transformation of energy from prey to predator is not instantaneous. The essential mathematical analysis with the help of equilibria, stability analysis and Hopf bifurcation theory are studied. By applying the normal form theory and the center manifold theorem, the direction of Hopf bifurcation is determined. To verify analytical findings, numerical experiments are done using biological meaningful parameter values. Results illustrate that the proposed system experiences Hopf bifurcation around positive equilibrium point when time delay crosses a sequence of critical values. These critical values can be controlled by supplying alternative resource as well as harvesting effort. The model can be applied in plankton and fishery management systems.

Acknowledgments

The authors are grateful to the editor and two anonymous honorable reviewers for their constructive comments and valuable suggestions which have immensely improved the content of this version.

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