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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Complex Dynamics of an Exploited Prey-PredatorModel with Nonlinear Prey Refuge

Discontinuity, Nonlinearity, and Complexity 9(1) (2020) 99--116 | DOI:10.5890/DNC.2020.03.008

Md. Manarul Haque, Sahabuddin Sarwardi

Department of Mathematics & Statistics, Aliah University, IIA/27, New Town, Kolkata - 700 160, India

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In this paper we study the renewable resources of a prey-predator system with prey refuge and nonlinear harvesting. Taxation is imposed to prevent over exploitations to maintain ecological balance. The steady state of the system are determined and various dynamical behavior are discussed in its steady states under certain parametric conditions. The boundedness, feasibility of interior equilibria, bionomic equilibrium have been studied. The main observation is that the taxation plays an important role in regulating the dynamics of the present system. Moreover the variation of the taxation change the system from periodic behaviors to chaos. Some numerical illustration are given in order to support of our analytical and theoretical findings.


The authors are grateful to the anonymous referees for their valuable comments and suggestions leading to possible improvement of this article. Authors are also thankful to the Department ofMathematics & Statistics, Aliah University for providing opportunities to perform the present work. The corresponding author Dr. S. Sarwardi is thankful to his Ph.D. supervisor Prof. Prashanta Kumar Mandal, Department of Mathematics, Visva-Bharati (a Central University) for his generous help and continuous encouragement while preparing this manuscript.


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