Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems

Lag synchronization of multiple identical Hindmarsh–Rose neuron models coupled in a ring structure

“…According to the Lyapunov stability theory, we know that the origin of error system (15) is asymptotically stable. Therefore, the multiple coupled Hindmarsh-Rose neuron system (14) achieves chaos synchronization with a time delay. The detailed synchronized conditions are shown in Appendix.…”

“…Experimental studies [7][8][9] have pointed out that the synchronization is significant in the information processing of large ensembles of neurons. Therefore, it is necessary to employ networks to investigate the dynamic complex spatiotemporal behavior of neural systems, and many studies have been carried out on synchronization in coupled bursting neuronal networks [10][11][12][13][14][15][16][17][18][19][20][21]. In [22], it was noted in three types of regular networks that the critical values depended on specific coupling styles when neurons achieved complete synchronization.…”

Synchronization of multiple bursting neurons ring coupled via impulsive variables

“…The dynamics of complex networks has been extensively investigated on the interplay between the local dynamical properties of the coupled nodes and the com-plexity in the overall topology [2][3][4][5][6]. As a typical kind of dynamics, synchronization of neuronal firing in networks has become of significant interest as a collective behavior possibly related to information transmission and processing in biological neurons [7][8][9][10][11][12]. So, the issue of synchronization in complex dynamical networks has become a rather significant topic in both theoretical research and practical applications (see Refs.…”

Phase synchronization in fractional differential chaotic systems

“…But no general necessary and sufficient condition for stability has yet been fully investigated, and the same observation would apply to phase synchronization until recently. Phase synchronization has been investigated in [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], for example, and more recently, fractional differential equations have been utilized to study dynamical systems in general and chaos and synchronization in particular [23][24][25][26][27][28][29]. It is well known that fractional differential equations are useful because of their non-local nature, whereas integer order (classical) differential equations that this property is the local one.…”