Self-synchronization of coupled chaotic FitzHugh–Nagumo systems with unreliable communication links

Oscillation analysis of the solutions for a four coupled FHN network model with delays

“…Let = 1 + 2 ( 2 may equal to zero) and = 1 + 2 ( 2 may equal to zero) ( = 1, 2, ..., 8) denote the eigenvalues of matrices and respectively. If for some , | 1 | < 1 , then the trivial solution of system (9) is unstable, implying that system (6) has an oscillatory solution.…”

“…Since all solutions of system (6) are bounded, according to Chafee's criterion, there exists an oscillatory solution of system (6). In the following, we consider the case that some ( = 1, 2, 3, 4) are not larger than zero.…”

“…With respect to system (1), a coupled FHN system may be able to better describe the dynamic characteristic such as its synchronization and stability. Therefore, the dynamic properties of various coupled FHN systems have recently been investigated by many researchers for better understanding about their collective behavior [2][3][4][5][6][7]. In 2009, Wang et al have investigated a coupled FHN neural model as follows [2]:…”

Lyapunov-based synchronization of two coupled chaotic Hindmarsh-Rose neurons

“…Following the first approach, many studies have confirmed that when the intensity of an internal noise exceeds a critical value, the self-synchronization can be achieved [12][13][14]. Other numerical results have shown that strong coupling can also synchronize a system of two FitzHugh-Nagumo neurons [15][16][17]. Also, the effect of difference in coupling strengths caused by the unidirectional gap junctions and the impact of time delay due to separation of neurons on the coupled FitzHugh-Nagumo neurons has been investigated [18].…”

“…In neuroscience, most investigations have focused on the synchronization of two coupled neurons, whose resolution aids in the understanding of the synchronization processes in neural networks [12-31, and reference therein]. The synchronization between interacting neurons can be classified into two types: the first pertains to natural coupling, in which the effects of the synapse types and internal noises on synchronization (self-synchronization) are issues [12][13][14][15][16][17][18]; the second pertains to artificial coupling, in which an explicit control signal is applied in order to archive synchronization [18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Following the first approach, many studies have confirmed that when the intensity of an internal noise exceeds a critical value, the self-synchronization can be achieved [12][13][14].…”