Synchronization stability for recurrent neural networks with time-varying delays

Abstract

This paper studies the general decay synchronization (GDS) of a class of recurrent neural networks (RNNs) with general activation functions and time-varying delays. By constructing suitable Lyapunov-Krasovskii functionals and employing useful inequality techniques, some sufficient conditions on the GDS of considered RNNs are established via a type of nonlinear control. In addition, an example with numerical simulations is presented to illustrate the obtained theoretical results.

General decay synchronization stability on the nonautonomous BAM recurrent neural networks with delays

“…It is worth noting that synchronization is a typical dynamical property of neural networks and presents major concerns when we investigate the dynamical behaviors of chaotic neural networks. Recently, the research on the synchronization of neural networks (NNs) model has attracted a lot of attention [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] as there are many benefits of having synchronization in some engineering applications such as language emergence and development, harmonic oscillation generation, secure communication, and information science. Moreover, synchronization, as a typical collective behavior, has been observed in biological systems such as synchronous fireflies, flocking of birds, and swarming of fish.…”

“…Moreover, recently in [18,19], a new concept of synchronization, namely general decay synchronization (GDS), was introduced for a class of chaotic NNs. Up to now, there have been many studies related to the study of GDS problems for various kinds of neural net-works with time delays and the references cited therein [18][19][20][21][22][23][24][25][26][27]. For example, the study of general decay synchronization for time-varying delayed and mixed time delayed recurrent neural networks [18][19][20][21], time-varying delayed and mixed time delayed BAM neural networks [22,23], delayed memristor-based Cohen-Grossberg neural networks [24], time-varying delayed fuzzy cellular neural networks [25], discrete time delayed competitive neural networks [26], and time-varying delayed complex multilink dynamic networks [27], are considered.…”

Synchronization on the non-autonomous cellular neural networks with time delays

“…But the intrinsic parameters of the non-autonomous NNs are variables and have input effect. Up to now, the majority of existing results are devoted to the autonomous NNs [12]- [26], and there are few papers considered the non-autonomous NNs [27,28]. In [27,28], the authors considered the following non-autonomous cellular neural networks(CNNs) with time variable delays and infinite delayṡ…”

“…Recently, a new concept of the synchronization, namely, the general decay synchronization (GDS) was introduced for a class of chaotic NNs by Wang, Shen and Zhang [24,25] and this GDS can deal with the above mentioned problem. There has been some literatures related to the study of the general decay synchronization for neural networks with time delays [21]- [26]. However, these models in [21]- [26] are all autonomous and without infinite delays.…”

“…There has been some literatures related to the study of the general decay synchronization for neural networks with time delays [21]- [26]. However, these models in [21]- [26] are all autonomous and without infinite delays. Besides, there is no theoretical result published on the research on the general decay synchronization for delayed cellular neural networks with time-varying coefficients and infinite delays.…”