Global exponential synchronization of fuzzy cellular neural networks with delays and reaction–diffusion terms

Attraction of Li–Yorke chaos by retarded SICNNs

“…The presence of chaos in neural networks is useful for separating image segments [8], information processing [12,13] and synchronization of neural networks [25][26][27][28][29][30]. Besides, the synchronization phenomenon is also observable in the dynamics of coupled chaotic CNNs [31,32].…”

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

“…Remark 2 If we set σ (t, e(t, x), e(t − τ (t), x)) = 0, the synchronization problem for reaction-diffusion neural networks without stochastic perturbation has been studied in [7,11,20,34,37,41]. However, the results of these are not presented in terms of LMIs, which makes their checking by the developed algorithms somewhat difficult and inconvenient.…”

“…In [20,37], the problem of asymptotic synchronization of delayed reactiondiffusion neural networks was studied with feedback control approach; adaptive exponential synchronization of reaction-diffusion neural networks was discussed in [11]. When Dirichlet boundary conditions of diffusion equation were considered, sufficient synchronization conditions were presented in [7,34,41]. The synchronization problem was investigated under the impulsive control in [7], where the proposed criterion was based on the p-norm.…”

“…By using the Lyapunov functional method, results on exponential synchronization of reaction-diffusion neural networks were provided in [34]. When fuzzy logic in the structure of networks appears, the synchronization criteria were presented in [41], in which the effect of reactiondiffusion was considered. It is worth noting that all of the above reported conditions are derived by certain inequality technique and expressed in the form of algebraic inequalities, which makes their checking somewhat difficult and inconvenient by the developed algorithms.…”

Stability analysis for periodic solutions of fuzzy shunting inhibitory CNNs with delays

“…By means of direct Lyapunov method, exponential stability of FCNNs with different types of delays, diffusion and impulsive perturbations were established in many papers including [12][13][14][15][16][17][18][19][20][21][22][23]. Furthermore, the synchronization of FCNNs was considered in the studies [24][25][26][27][28][29][30]. On the other hand, from an application point of view, one is interested in a periodic or an almost periodic solution of FCNNs.…”