Application of differential transformation method for solving prey predator model with holling type I

Abstract

Nonlinear differential equations are used for describing many phenomena in the real world as prey predator interactions.  Prey predator models are classified as one of the most important applications in applied mathematics.  In this paper, modified structure of prey predator model is used, theoretical properties of the model are presented, the boundedness of the model is shown and the dynamical behavior of the model is proved as globally stable.  Semi analytical solution by using differential transformation method (DTM) is obtained for non-dimensional prey predator model with Holling type I in the case of persistence dynamics of the model.  The results seem to satisfy biological domain of the problem.  We conclude that the results of differential transformation method is in good agreement with numerical results from interpolation method (IM) by using MATHEMATICA program.