Abstract
This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.
Highlights
In recent decades, behavior investigation of chaotic neurons including synchronization, under external electrical stimulation (EES; e.g., deep brain stimulation), has become an important area of research in the study of clinical treatment mechanisms for neurodegenerative disorders [1, 2]
Synchronization of two identical neurons of unknown parameters, under uncertain stimulation currents caused by medium losses and phase shifts, has been explored by application of an adaptive control scheme [14]
This paper addressed the synchronization of two coupled chaotic FHN neurons for different and unknown parameters under uncertain external stimulation and disturbances
Summary
Behavior investigation of chaotic neurons including synchronization, under external electrical stimulation (EES; e.g., deep brain stimulation), has become an important area of research in the study of clinical treatment mechanisms for neurodegenerative disorders [1, 2]. Robust adaptive control schemes for synchronization of two or three FHN neurons of unknown model parameters have been developed as well. Synchronization of two identical neurons of unknown parameters, under uncertain stimulation currents caused by medium losses and phase shifts, has been explored by application of an adaptive control scheme [14]. This paper analyzes the behavior and synchronization of two different coupled distant FHN neurons under unidirectional gap junctions. The design of robust adaptive control laws for synchronization of coupled chaotic distant FHN neurons under unidirectional gap junctions is addressed. (v) The proposed synchronization control methodology fills the research gap on robust adaptive synchronization of FHN neurons of different and unknown parameters subject to disturbances. The notation ‖ ⋅ ‖ symbolizes the Euclidian norm of a vector
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