Abstract
In this article we discuss the dynamical behavior of a modified Leslie–Gower prey–predator model in presence of nonlinear harvesting in prey under the assumption that the protection provided by environment to prey and predator is different. The objective of this work is to find the parametric conditions so that extinction of the species can be prevented in presence of continuous harvesting of the prey population. We analyze the effect of harvesting on the proposed model by considering the harvesting as a bifurcation and control parameter. The existence and stability of equilibrium points are discussed and singular optimal control has been derived through Pontryagin’s Maximum Principle. This study provides important tools for investigations pertaining to controllability of the system. Numerical simulations using MATLAB are carried out as supporting evidences of our analytical findings.
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Gupta, R.P., Chandra, P. (2016). Dynamical Behavior of a Modified Leslie–Gower Prey–Predator Model with Michaelis–Menten Type Prey-Harvesting. In: Cushing, J., Saleem, M., Srivastava, H., Khan, M., Merajuddin, M. (eds) Applied Analysis in Biological and Physical Sciences. Springer Proceedings in Mathematics & Statistics, vol 186. Springer, New Delhi. https://doi.org/10.1007/978-81-322-3640-5_6
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DOI: https://doi.org/10.1007/978-81-322-3640-5_6
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