Two effective computational schemes for a prototype of an excitable system
Mostafa M. A. Khater, Choonkil Park, Dianchen Lu
Abstract
In this article, two recent computational schemes [the modified Khater method and the generalized exp−φ(I)–expansion method] are applied to the nonlinear predator–prey system for constructing novel explicit solutions that describe a prototype of an excitable system. Many distinct types of solutions are obtained such as hyperbolic, parabolic, and rational. Moreover, the Hamiltonian system’s characteristics are employed to check the stability of the obtained solutions to show their ability to be applied in various applications. 2D, 3D, and contour plots are sketched to illustrate more physical and dynamical properties of the obtained solutions. Comparing our obtained solutions and that obtained in previous published research papers shows the novelty of our paper. The performance of the two used analytical schemes explains their effectiveness, powerfulness, practicality, and usefulness. In addition, their ability in employing various forms of nonlinear evolution equations is also shown.