The Multistage Homotopy Perturbation method for solving Hyperchaotic Chen system

Abstract

Finding accurate and efficient methods for solving nonlinear hyper chaotic problems has long been an active research undertaking. Like the well-known Adomian decomposition method (ADM) and based on observations, it is hopeless to find HPM solutions of hyper chaotic systems valid globally in time. To overcome this shortcoming, we employ the multistage homotopy-perturbation method (MHPM) to the nonlinear hyperchaotic Chen system. Based on the cases investigated, MHPM is more stable for a longer time span than the standard HPM. Comparisons with the standard HPM and the well-known purely numerical fourth-order Runge-Kutta method (RK4) suggest that the MHPM is a powerful alternative for nonlinear hyper chaotic system. The new algorithm and the new technique for choosing the initial approximations were shown to yield rapidly convergent series solutions.