Existence and global exponential stability of equilibrium of competitive neural networks with different time scales and multiple delays

Synchronization for competitive neural networks by output feedback and impulsive control

“…For ∈ [ −1 , ), taking the time derivative of the Lyapunov functional (14) along the trajectories of (11), we havė…”

“…However, the delays are often different. To our knowledge, such neural networks with multiple delays have been reported in a few literatures [13,14,25,31,32].…”

Improved exponential stability analysis for delayed recurrent neural networks

“…Recurrent neural networks including Hopfield neural networks (HNNs) and cellular neural networks (CNNs) have been studied extensively over the recent decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and have been widely applied within various engineering fields such as neuro-biology, population dynamics, and computing technology. When neural networks are applied to signal processing and pattern classification systems or to the solution of nonlinear algebraic equations and optimization problems, it is necessary to establish the existence of a unique equilibrium point and to determine its qualitative properties of stability.…”

“…Accordingly, the problem of global exponential stability analysis for delayed neural networks has been studied by many investigators in the past years. In [6], some sufficient conditions are obtained for existence and global exponential stability of a unique equilibrium point of competitive neural networks. The exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type was studied in [20] using an appropriate Lyapunov functional.…”

Aτ-type stability criteria in division regions for multitime-scale networks with delays

“…It is worth noting that there exist interesting topics about multistability research for muititime‐scale competitive neural networks : The existing ones incorporated global Lipschitz condition into convergent criteria and attained monostability results. Some new multistable dynamics could not be directly revealed by using the existing approaches. Sigmoidal or piecewise linear activation properties are employed in and for multistability analysis of muititime‐scale competitive networks.…”