Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 72, Issue 5, Pages 2326-2336Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2009.10.033
Keywords
Fractional order; Qi oscillator; Chaotic synchronization; Master-slave
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Funding
- Ministry of Education of PR China [107110]
- Chinese National Natural Science Foundation [90916003]
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In this paper, a special kind of nonlinear chaotic oscillator, the Qi oscillator, is studied in detail. Since such systems are shown to possess a relatively wide spectral bandwidth, it is considerably beneficial to practical engineering in the secure communication field. The chaos synchronization problem of the fractional-order Qi oscillators coupled in a master-slave pattern is examined by applying three different kinds of methods: the nonlinear feedback method, the one-way coupling method and the method based on the state observer. Suitable synchronization conditions are derived by using the Lyapunov stability theory, and most importantly, a sufficient and necessary synchronization condition for the case with fractional order between 1 and 2 is presented. Results of numerical Simulations validate the effectiveness and applicability of the proposed schemes. (C) 2009 Elsevier Ltd. All rights reserved.
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