Variational Iteration Method for Hyperchaotic Nonlinear Fractional Differential Equations Systems

摘要

The aim of this paper is to obtain solutions for the hyper-chaotic nonlinear fractional differential equations system given by, D_t~α u(t)=au(t)-y(t) D_t~α y(t)=u(t)-y(t)z~2 (t) (1) D_t~α z(t) = -b_1y(t)-b_2z(t)-b_3w(t) D_t~α w(t)= z(t)+cw(t), under the starting conditions, u(0) = β_1, y(0) = β_2, z(0) = β_3, w(0) = β_4. (2) To this end, the variational iteration method is theoretically implemented and numerically executed only to yield the desired solutions, of which graphical plots are exhibited. While the obtained results show the effectiveness of the theoretical tools used, they also shed much light on the dynamic behaviour of the hyper-chaotic system at hand.