Dynamics of a fractional-order simplified unified system based on the Adomian decomposition method

Yixin Xu; Kehui Sun; Shaobo He; Limin Zhang

doi:10.1140/epjp/i2016-16186-3

EPJ

Dynamics of a fractional-order simplified unified system based on the Adomian decomposition method

Yixin Xu¹, Kehui Sun¹^,2^*, Shaobo He¹ and Limin Zhang¹

¹ School of Physics and Electronics, Central South University, 410083, Changsha, China
² School of Physics Science and Technology, Xinjiang University, 830046, Urumqi, China

Received: 3 February 2016
Accepted: 3 May 2016
Published online: 3 June 2016

Abstract

In this paper, the Adomian decomposition method (ADM) is applied to solve the fractional-order simplified unified system. The dynamics of the system is analyzed by means of the Lyapunov exponent spectrum, bifurcations, chaotic attractor, power spectrum and maximum Lyapunov exponent diagram. Route to chaos by period doubling is observed. Chaos is found to exist in the system with order as low as 1.371. In addition, chaotic behaviors are studied with different dimensional order, and the results show that this system is chaotic when only the first or third dimension is fractional.