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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

Spatiotemporal patterns of a pursuit-evasion generalist predator-prey model with prey harvesting

Journal of Applied Nonlinear Dynamics 7(2) (2018) 165--177 | DOI:10.5890/JAND.2018.06.005

Lakshmi Narayan Guin; Benukar Mondal; Santabrata Chakravarty

Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Bengal, India

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Abstract

The present investigation deals with a diffusive predator-prey model in order to study the dynamic response of a reaction-diffusion model with linear prey harvesting. The governing equations of the proposed model system subject to the homogeneous Neumann boundary condition provide some qualitative interpretations of solutions to the reaction-diffusion system. The conditions of diffusion-driven instability and the Turing bifurcation region in two parameter space are explored. From the outcome of the present mathematical analysis carried out followed by the numerical simulations based on the model parameters, it reveals that for unequal diffusive coefficients, prey harvesting may induce that diffusion-driven instability resulting in stationary Turing patterns. The choice of parameter values is important to study the effect of prey harvesting and diffusion, while it depends more on the non-linearity of the model system. Moreover, the model dynamics exhibits the influence of both prey harvesting and diffusion controlled pattern formation growth to holes, stripes-holes mixture, stripes, labyrinthine, stripes-spots mixture and spots replication. All these features illustrate that the dynamics of the proposed model with the control of prey harvesting is not straightforward, but rich and complex in nature.

Acknowledgments

The authors are thankful to the learned referees for their valuable comments and suggestions towards an improvement of the present paper. The authors also gratefully acknowledge the financial support in part from Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.510 / 3 / DRS-III / 2015 (SAP-I)).

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