Sustaining stable dynamics of a fractional-order chaotic financial system by parameter switching

Authors:
Marius-F. Danca;Roberto Garrappa;Wallace K. S. Tang;Guanrong Chen
Affiliations:
Department of Mathematics and Computer Science, Avram Iancu University, 400380 Cluj-Napoca, Romania and Romanian Institute of Science and Technology, 400487 Cluj-Napoca, Romania;Department of Mathematics, University of Bari, 70125 Bari, Italy;Department of Electronic Engineering, City University of Hong Kong, Hong Kong;Department of Electronic Engineering, City University of Hong Kong, Hong Kong
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

In this paper, a simple parameter switching (PS) methodology is proposed for sustaining the stable dynamics of a fractional-order chaotic financial system. This is achieved by switching a controllable parameter of the system, within a chosen set of values and for relatively short periods of time. The effectiveness of the method is confirmed from a computer-aided approach, and its applications to chaos control and anti-control are demonstrated. In order to obtain a numerical solution of the fractional-order financial system, a variant of the Grunwald-Letnikov scheme is used. Extensive simulation results show that the resulting chaotic attractor well represents a numerical approximation of the underlying chaotic attractor, which is obtained by applying the average of the switched values. Moreover, it is illustrated that this approach is also applicable to the integer-order financial system.