Observer of a class of chaotic systems: An application to Hindmarsh–Rose neuronal model

Abstract

This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh–Rose (HR) neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.

Chaotic dynamics and its analysis of Hindmarsh–Rose neurons by Shil’nikov approach

“…[5]. Adaptive control approaches, [6] an exponentially fast synchronization approach, [7] and an observer-based synchronization approach [8] are also developed to realize the synchronization of two HR neurons. Such simulation results are beneficial to experiments.…”

Synchronization of coupled chaotic Hindmarsh Rose neurons: An adaptive approach

“…[15][16][17] For the second synchronization mechanism, a variety of synchronization approaches have been proposed to synchronize the aforementioned neural systems. [18][19][20][21][22][23][24][25][26] In Ref. [18], H ∞ variable universe adaptive fuzzy control is utilized to synchronize the HH neurons.…”

“…[18], H ∞ variable universe adaptive fuzzy control is utilized to synchronize the HH neurons. Adaptive neural network H ∞ control, [19] state observer based control, [20,21] nonlinear feedback control, [22][23][24] robust adaptive sliding mode control, [25] and adaptive control [26] have been utilized to realize the synchronization of various neural systems. In addition, a novel master-slave coupling, which exists between the membrane potential of the master neuron and the slow ion kinetics of the slave neuron, other than classical synchronization of two neurons modeled as electrical and chemical coupling in action potential variables, enables the synchronization between neurons.…”

“…Two identical HR neuronal chaotic systems are synchronized by a state observer-based control. [20] An adaptive control approach [26] is proposed to synchronize two HR neurons with unknown parameters. However, no disturbance is considered in those synchronizations.…”