Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

By Yurong Liu, Zidong Wang, Xiaohui Liu. Neural Networks, 2006

694 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/5b61845548705a65a7d182e2ff7c36ff4374bab8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Huaguang Zhang
2. Derong Liu
3. Jinling Liang
4. Zhanshan Wang
5. Zidong Wang
6. Xiaohui Liu
7. Yurong Liu
8. Peng Shi

In Computer Networks and Communications

1. Zidong Wang
2. Xiaohui Liu
3. Jinling Liang
4. Jinde Cao
5. Yurong Liu
6. Guanrong Chen
7. Huaguang Zhang
8. Wenwu Yu

In Electrical and Electronic Engineering

1. Derong Liu
2. Huaguang Zhang
3. Zhanshan Wang
4. Zidong Wang
5. Xiaohui Liu
6. Jinling Liang
7. Peng Shi
8. Zhengguang Wu

Citations in the corpus

• Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays (2009, background): “Assumption 2 [21] , [22]: For the activation functions , , and , there exist constants , , , , , and such that (3) (4) (5) Remark 2: As pointed out in [21] and [22], the constants , , , , , and in Assumption 2 are allowed to be positive , negative, or zero.”
• Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays (2008, neutral): “Assumption 1: The nonlinear vector-valued functions f , g, and h are continuous and satisfy [20], [33] [f(x) − f(y) − B1(x − y)] [f(x) − f(y) − B2(x − y)] ≤ 0 ∀ x, y ∈ R (7) [g(x) − g(y) − D1(x − y)] [g(x) − g(y) − D2(x − y)] ≤ 0 ∀ x, y ∈ R (8) [h(x) − h(y) − V1(x − y)] [h(x) − h(y) − V2(x − y)] ≤ 0”
• A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks (2014, background): “(19) 5) The following activation functions are developed in [43], [135], [138], [139], [176], [177], [242], [294], and [304]: δ − i ≤ g i (ζ ) − g i (ξ ) ζ − ξ ≤ δ + i .”
• Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling (2008, background): “Hence, it is necessary to take into account both discrete and distributed time delays [32]–[34].”
• Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays (2011, background): “Assumption 1 [ 6 ]: Each activation function gi (·) in (1) is continuous and bounded, and there exist constants δi and ρi such that δi ≤ gi (α1) − gi (α2) α1 − α2 ≤ ρi , i = 1, 2 ,..., n (5)”
• Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data (2013, background): “Throughout this paper, we make the following assumption: Assumption 1 [16]: Each activation function gi(·) in (1) is continuous and bounded, and there exist constants F− i and F + i such that”
• Exponential synchronization of complex networks with Markovian jump and mixed delays (2008, neutral): “(A2) [20,34,35] For ∀x, y ∈ Rn, i ∈ {1, 2, .”
• Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays (2010, neutral): “Accordingly, the synchronization problem for continuous-time complex networks with discrete and/or distributed time delays has been extensively investigated in [ 17 ] and [18].”
• Exponential synchronization of stochastic delayed discrete-time complex networks (2008, methodology): “Remark 1 Compared to the earlier network models discussed in [4, 11, 15–17], in this paper, we have dropped the external input vector I in system (1) without loss of any generality.”