Parameters estimation, mixed synchronization, and antisynchronization in chaotic systems

Abstract

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 3 10 26 , whereas the smallest unknown parameter is approached greatly although the error of corresponding variables are stabilized within certain transient period.

Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system

“…In this paper, it is assumed that all parameters can be obtained accurately. Future research will extend the proposed control method to high-order system with unknown parameters and improve it by introducing adjustable gain coefficient into controller, parameter observer and Lyapunov function similar to [58,59].…”

Detection of noise effect on coupled neuronal circuits

“…The Hindmarsh-Rose neuron model [2,55,56] is a simplified mathematical model, which can reproduce the main dynamical properties of neuron, and it is effective for bifurcation analysis. The dynamical equations can be described as follows 3 2…”

FPGA realization of a chaotic communication system applied to image processing

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