WSEAS Transactions on Biology and Biomedicine
Print ISSN: 1109-9518, E-ISSN: 2224-2902
Volume 10, 2013
Numerical-Analytical Solutions of Predator-Prey Models
Authors: , ,
Abstract: This paper deals with the construction of piecewise analytic approximate solutions for nonlinear initial value problems modeled by a system of nonlinear ordinary differential equations. In real world several biological and environmental parameters in the predator-prey model vary in time. Thus, non-autonomous systems are impor- tant to be studied. We show the effectiveness of the method for autonomous and non-autonomous predator-prey systems. The method we have used is called the differential transformation method which has some suitable prop- erties such as accuracy, low computational cost, easiness of implementation and simulation as well as preserving properties of the exact theoretical solution of the problem. The accuracy of the method is checked by numerical comparison with fourth-order Runge-Kutta results applied to several predator-prey examples.
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Keywords: Differential transformation method, Population dynamics, Nonlinear differential system, Predator-prey system