Abstract
The use of mathematical models in prey predator interplay is common to solve the interdisciplinary natural problems. This paper reports analytical advancement of measuring selective harvesting activity of prey proportional to their population size and studied the stability of the model using Holling type functional response. In this paper, we analysed four prey-predatory model and considered prey and predator as a X and Y axis respectively followed by applied variational matrix and Holling I and II type response function for equilibrium and local stability measurement. Simulation experiments were carried out. Further, numerical analysis was done with help of MATLAB packages at MS window 7. Analysis of result showed prey and predator population converges asymptotically to their equilibrium values when t (time) tends to infinity and corresponding spiral phase portraits obtained. Interestingly analysis of result showed the behaviour of prey and predator with respect to time and phase portrait of the system near the equilibrium point. Above analysis indicated that application of vibrational matrix and holing type response function give better understand ability of prey predator interplay of biological forces
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