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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 127404, 12 pages
http://dx.doi.org/10.1155/2015/127404
Research Article

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

1Institute of Mathematics and Computer Science, Zunyi Normal University, Zunyi 563000, China
2Department of Basic Education, Business School of Guizhou University of Finance and Economics, Huishui 550600, China
3School of Mathematics and Information Science, North University of Nationalities, Yinchuan 750021, China

Received 6 October 2015; Revised 9 November 2015; Accepted 19 November 2015

Academic Editor: Daniele Fournier-Prunaret

Copyright © 2015 Jie Ran et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.