Discontinuity, Nonlinearity, and Complexity
Complex Dynamics of an Exploited PreyPredatorModel with Nonlinear Prey Refuge
Discontinuity, Nonlinearity, and Complexity 9(1) (2020) 99116  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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Abstract
In this paper we study the renewable resources of a preypredator 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.
Acknowledgments
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, VisvaBharati (a Central University) for his generous help and continuous encouragement while preparing this manuscript.
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