Finite-time synchronization of competitive neural networks with mixed delays

Abstract

In this paper, finite-time synchronization of competitive neural networks (CNNs) with bounded time-varying discrete and distributed delays (mixed delays) is investigated. A simple controller is added to response (slave) system such that it can be synchronized with the driving (master) CNN in a setting time. By introducing a suitable Lyapunov-Krasovskii's functional and utilizing some inequalities, several sufficient conditions are obtained to ensure the control object. Moreover, the setting time is explicitly given. Different from previous results, the setting is related to both the initial value of error system and the time delays. Finally, numerical examples are given to show the effectiveness of the theoretical results.

Global exponential convergence and synchronization for exponential numerical competitive neural networks with different time scales and fuzzy logic

“…Thus STM means rapid neural activity, while LTM represents the unsupervised slow activity of synaptic modifications induced by inputs. For the past few years, many researchers have investigated the problems of synchronization and stability of CNNs, as well as other dynamical behaviors, please see papers [14][15][16][17][18][19][20] for more information.…”

“…[32][33][34] Accordingly, it has important theoretical and practical relevance to research the synchronization of CNNs, in which numerous interesting works were explored in literatures. 14,15,[18][19][20] Difference systems can be preferably implemented in the practical applications. It possesses some advantages for the difference configurations.…”

Attractivity of saturated equilibria for Lotka-Volterra systems with infinite delays and feedback controls

“…Recently, there has been a significant number of publications on the study of Lotka-Volterra population models with delays and feedback controls, see [6,13,19,22,27,28,30,31,32,37,38] and references cited therein. In particular, Li et al [22] established results on the influence of the feedback controls on extinction and global attractivity of a two-species autonomous competitive Lotka-Volterra system with infinite delays by applying Lyapunov functional techniques.…”

New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

“…Since, in reality, time delays cannot be avoided and it is well known that the dynamics of neural networks plays a crucial role in their implementation and applications, recently, many researchers have paid much attention to the dynamics analysis of neural networks with various types of delays [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For example, the authors of [17][18][19][20][21][22][23][24] studied the global stability for CNNs; the authors of [23] investigated the multistability for CNNs; the authors of [24] investigated multistability and multiperiodicity of CNNs; the authors of [25] studied the existence and global exponential stability of anti-periodic solutions for CNNs; and the authors of [26][27][28] However, there are very few existing works dealing with the dynamics of CNNs with the proportional delay. Proportional delay is a kind of discrete delay, which is time-varying and unbounded.…”