Chaos synchronization for a class of nonlinear oscillators with fractional order

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.