Projective synchronization of different chaotic neural networks with mixed time delays based on an integral sliding mode controller

Attraction of Li–Yorke chaos by retarded SICNNs

“…We prove that the Li-Yorke chaos is extended with its ingredients, proximality and frequent separation, which have not been considered in the theory of synchronization at all. (iv) Our results can be extended in neuroscience by specific stability analysis methods, for example, by the linear matrix inequality technique [25,[107][108][109][110].…”

“…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].…”

An approach to achieve modified projective synchronization between different types of fractional-order chaotic systems with time-varying delays

“…Consider the following chaotic drive and response systems as (14) and (15) where x r , x d ∈ R n are n-dimensional state vectors for drive and response systems respectively, f is a continuous vector function to describe the drive system, g is a continuous vector function for the response system, α are R n vectors to denote the fractional-orders for each state of the drive and response systems, respectively, α = [α 1 , α 2 , · · · , α n ] T , α i ∈ (0, 1]. Note that one of the premises of the proposed approach implies a condition 0 < α i ≤ 1.…”

“…For the fractional order time-delayed drive system (14) and response system (15), it is said to be modified projective synchronization if there exists a controller U such that…”

“…There are many investigations on the synchronization of two identical or different fractional-ordered chaotic systems without delays [6][7][8][9][10]. The control and synchronization of time-delay systems have received increasing attentions [11][12][13][14]. However, there are few results in the synchronization of a fractional-order chaotic systems with time delay [15] also there is not any specific study on synchronization of time-delay fractionalorder chaotic systems with time-varying time delay.…”