Proiective SVnehtonization of One Fractional—order Chaotie SVstem

KONG De-fu

(College of science， Tianjin University of Technology and Education， Tianjin 300222， China)

【Abstract】In this paper, projective synchronization of one fractional-order chaotic system is studied. Firstly, the chaotic attractor is given. Then, suitable projective synchronization controllers are investigated based on the Lyapunov stability theory. Finally, the numerical simulations verify the validity and correction of the method.

【Key words】Fractional-order chaotic system; Projective synchronization; Controller

0Introduction

Chaos synchronization have received lots of attention in last few decades due to its potential applications in chemical reactions, biological systems, information processing, secure communications, etc[-5]. Many methods and techniques have been developed, such as OGY method[6], PC method[7-8], feedback approach, adaptive method and backstepping design technique, etc. In this work projective synchronization of one fractional-order chaotic system is investigated. A reasonable controller is designed and proved by Lyapunov stability theory. At last, numerical simulation coincide with the theoretical analysis.

１System description

where x，y，z are the state variables. The chaotic attractors of the system for the order of derivative q=0.98 are displayed through Fig.1 for the parameters，values ɑ=100, b=0.1, c=1.6, d=200.

４Conclusion

In this letter, projective synchronization of one fractional-order chaotic system is presented, and the chaotic attractor is given. Besides, suitable synchronization controllers are investigated by using the Lyapunov stability theory. Numerical simulations are performed to verify these results.

【Reference】

［１］Yang T, Chua LO. Secure communication via chaotic parameter modulation[J]. IEEE Trans Circuits Syst I, 1996,43:817-819.

［２］Feki M. An adaptive chaos synchronization scheme applied to secure communication[J].Chaos Soliton Fract, 2003,3:959-964.

［３］Li C, Liao X, Wong K. Chaotic lag synchronization of coupled time-delayed systems and its application in secure communication[J]. Physica D, 2004,194:187-202.

［４］Chang WD. Digital secure comumunication via chaotic systems[J]. Digital Signal Process, 2009,19:693-699.

［５］Nana B, Woafo P, Domngang S. Chaotic synchronization with experimental application to secure communication[J].Commun Nonlinear Sci Numer Simul,2009,14:2266-2276.

［６］Ott E, Grebogi C, Yorke JA. Controlling chaos[J].Phys. Rev. Lett., 1990,64:1196-1199.

［７］Pecora LM, Carroll TM. Synchronization of chaotic system[J]. Phys Rev Lett.,1990,64(8):821-830.

［８］Carroll TL, Pecora LM. Synchronizing a chaotic systems, IEEE Trans Circuits Sys., 1991,38:453-456.

［９］W. Hahn. The Stability of Motion[M]. Springer, New York, 1967.

［责任编辑：邓丽丽］