Parameters estimation, mixed synchronization, and antisynchronization in chaotic systems

Mixed synchronization between two Hindmarsh-Rose neuron models is realized by optimizing the scheme of Lyapunov function with two selectable gain coefficients. Based on the Lyapunov stability theory, the distribution of synchronization region and the nonsynchronization region in the two-parameter phase space is calculated, respectively. And then the optimized parameter observers and controllers are approached analytically. All unknown parameters with different orders of magnitude are identified accurately, and the error function for corresponding variables decreases to stable value when the two gain coefficients are given values in the synchronization region. Otherwise, only the four larger unknown parameters are estimated exactly and the error function of corresponding variables decreases stably to certain minimal value with an order about 1 × 10-6, whereas the smallest unknown parameter is approached greatly although the error of corresponding variables are stabilized within certain transient period. © 2014 Wiley Periodicals, Inc. Complexity 20: 64-73, 2014

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