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Jana S.,Bengal Engineering and Science University | Chakraborty M.,Golahat Jr. High School | Chakraborty K.,Information Services Group | Kar T.K.,Bengal Engineering and Science University
Mathematics and Computers in Simulation | Year: 2012

This paper describes a prey-predator model with Holling type II functional response incorporating prey refuge. The equilibria of the proposed system are determined and the behavior of the system is investigated around equilibria. Density-dependent mortality rate for the predator is considered as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the co-existing equilibrium point. Discrete-type gestational delay of predators is also incorporated on the system. The dynamics of the delay induced prey-predator system is analyzed. Delay preserving stability and direction of the system is studied. Global stability of the delay preserving system is shown. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations. © 2012 IMACS. Published by Elsevier B.V. All rights reserved.

Chakraborty K.,Information Services Group | Chakraborty M.,Golahat Jr. High School | Kar T.K.,Bengal Engineering and Science University
Journal of Biological Systems | Year: 2014

This paper deals with the surplus production models of Verhulst-Schaefer and Gompertz-Fox that are applied to the European Hake fishery to develop static as well as dynamic frameworks to investigate the sustainability properties of the stock, optimal utilization of the resource and the management of the fishery. To illustrate the approach through which long-run sustainability can achieve an optimum exploitation of the fishery, a conventional economic model is combined with a biological population growth model to develop a deterministic bioeconomic model. The parameters of the bioeconomic model are estimated using empirical data of catch and effort of the European Hake fishery. Standard reference points are analyzed and tax policies are introduced to attain the standard reference points. In order to achieve maximum profit from the fishery, optimal steady state solutions are determined for separate discount rates. © 2014 World Scientific Publishing Company.

Das K.,Sashinara High School | Chakraborty M.,Golahat Jr. High School | Chakraborty K.,Information Services Group | Kar T.K.,Indian Institute of Science
Nonlinear Dynamics | Year: 2014

This paper describes a multiple delayed modified Leslie–Gower type predator–prey system with a strong Allee effect in prey population growth. Non-selective effort is used to harvest the population. The dynamical characteristics of the delay induced system are rigorously studied using mathematical tools. The existence of coexistence equilibria is ensured, and the dynamic behavior of the system is investigated around coexistence equilibria. Uniform strong persistence and permanence of the system are discussed in order to ensure long-term survival of the species. The stability of the delay preserved system is investigated. Sufficient conditions are derived for local and global stability of the system. The existence of Hopf bifurcation phenomenon is examined around interior equilibria of the system. Subsequently, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. Finally, numerical simulations are carried out to validate the analytical findings. © 2014, Springer Science+Business Media Dordrecht.

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