Attractivity Analysis of Memristor-Based Cellular Neural Networks With Time-Varying Delays

Abstract

This paper presents new theoretical results on the invariance and attractivity of memristor-based cellular neural networks (MCNNs) with time-varying delays. First, sufficient conditions to assure the boundedness and global attractivity of the networks are derived. Using state-space decomposition and some analytic techniques, it is shown that the number of equilibria located in the saturation regions of the piecewise-linear activation functions of an n-neuron MCNN with time-varying delays increases significantly from 2(n) to 2(2n2)+n) (2(2n2) times) compared with that without a memristor. In addition, sufficient conditions for the invariance and local or global attractivity of equilibria or attractive sets in any designated region are derived. Finally, two illustrative examples are given to elaborate the characteristics of the results in detail.

New results on synchronization control of delayed memristive neural networks

“…Recently, dynamic analysis of memristive neural networks has been attracted increasing attention; e.g., some sufficient conditions were obtained for stability or periodic solution [7][8][9][10][11][12][13], synchronization [14][15][16], dissipativity and attractivity [17][18][19].…”

“…The memristive neural network is a class of statedependent nonlinear systems from a systems-theoretic point of view [7][8][9][10][11][12][13][14][15][16][17][18][19]. Such system can reveal coexisting solutions, jumped, transient chaos of rich and complex nonlinear behaviors [14,16], and these problems bring challenges to investigate the exponential synchronization of such system.…”

Lag quasi-synchronization for memristive neural networks with switching jumps mismatch

“…For example, novel memristor-based cellular neural networks were designed in [5], in which the proposed cellular neural networks have high density, nonvolatility and programmability of synaptic weights. Recently, many efforts have been devoted to the dynamics of MNNs, because they not only have rich applications in signal, image processing and diversified applications elsewhere, but also can facilitate to simulate the real brain [9][10][11][12][13][14][15][16][17][18]. The synchronization problem of MNNs has attracted considerable attention due to its strong applications [19][20][21][22][23][24][25][26][27][28].…”

“…In secure communications, the MNNs chaotic is safer [12,20,23,[25][26][27]. In memory storage, the MNNs shall possess more memory storage capacity [10,11]. In associative memory and information processing, the computation power and information capacity can be substantially enhanced by using MNNs [14][15][16].…”

Stability of delayed neural networks with impulsive strength-dependent average impulsive intervals

“…Over the past few years, neural networks have been widely studied due to their potential applications in various fields, such as, robotic control, fault detection, system identification, image restoration and so on [2,10,13,18,24,25,[29][30][31][32]36]. In the implementation of neural networks, owing to the limited speed of signal propagation, time-varying delays are often encountered.…”