Title: Dynamics in harvested prey-predator mathematical model with noise and diffusion

Authors: K. Shiva Reddy; M.N. Srinivas; A. Sabarmathi; Kalyan Das; N.H. Gazi

Addresses: Department of Mathematics, School of Engineering, Anurag Group of Institutions, Hyderabad, India ' School of Advanced Sciences, V I T University, Vellore, India ' School of Advanced Sciences, V I T University, Vellore, India ' National Institute of Food Technology Entrepreneurship and Management, Department of Mathematics, Plot No. 97, Sector 56, HSIIDC Industrial Estate, Kundli-131 028, Haryana, India ' Aliah University, Department of Mathematics, DN 18, Salt Lake, Sector V, Kolkata 700091, India

Abstract: In the present study, we consider a two-dimensional nonlinear prey-predator model with harvesting on both the species and specifically with the mortality rate of the predator species. The purpose of this work is to offer mathematical analysis of the model and to discuss some of the vibrant qualitative results that are expected to arise from the inter-play of the biological internal and external forces. Here, all the possible equilibrium points of the model are identified and the criteria for the local as well as global stabilities are investigated. Apart from this, the existence of bio-economic equilibrium with optimal scheme has been critically discussed here. We studied the analytical estimates for the population intensities of fluctuations by Fourier transform methods through stochastic perturbations. We have also highlighted the diffusive stability of the system along with some numerical simulations.

Keywords: bionomic harvesting; optimal harvesting; predator-prey; stability; stochastic modelling; white noise; dynamics; mathematical modelling; diffusion; nonlinear modelling; mortality rate; bio-economic equilibrium; Fourier transform; numerical simulation.

DOI: 10.1504/IJDSDE.2016.074575

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.1, pp.36 - 62

Accepted: 18 Apr 2015
Published online: 05 Feb 2016 *

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