Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yiyuan Chai ◽  
Jiqiang Feng ◽  
Sitian Qin ◽  
Xinyu Pan
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Activation Functions ◽  
Functional Theory ◽  
Alternative Theorem ◽  
Discontinuous Activation ◽  
Inclusion Theory ◽  
Discontinuous Activation Functions

Abstract This paper is concerned with the existence and global exponential stability of the periodic solution of delayed Cohen–Grossberg neural networks (CGNNs) with discontinuous activation functions. The activations considered herein are non-decreasing but not required to be Lipschitz or continuous. Based on differential inclusion theory, Lyapunov functional theory and Leary–Schauder alternative theorem, some sufficient criteria are derived to ensure the existence and global exponential stability of the periodic solution. In order to show the superiority of the obtained results, an application and some detailed comparisons between some existing related results and our results are presented. Finally, some numerical examples are also illustrated.

scholarly journals Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yanyan Wang ◽  
Jianping Zhou
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Globally Exponential Stability ◽  
Discontinuous Activation Functions

Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property ofM-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.

scholarly journals Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Huaiqin Wu ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang ◽  
Luying Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Activation Functions ◽  
Robust Exponential Stability ◽  
Discontinuous Activation ◽  
Interval Neural Networks ◽  
Discontinuous Activation Functions ◽  
Global Robust Exponential Stability

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

Robust stability of mixed Cohen–Grossberg neural networks with discontinuous activation functions

2019 ◽  
Vol 12 (1) ◽  
pp. 82-101 ◽  
Author(s):  
Cheng-De Zheng ◽  
Ye Liu ◽  
Yan Xiao
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Integral Inequality ◽  
Sufficient Condition ◽  
Activation Functions ◽  
Content Type ◽  
Alternative Theorem ◽  
Discontinuous Activation ◽  
Discontinuous Activation Functions ◽  
Delay Dependent

PurposeThe purpose of this paper is to develop a method for the existence, uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays, continuous distributed delays and a kind of discontinuous activation functions.Design/methodology/approachBased on the Leray–Schauder alternative theorem and chain rule, by using a novel integral inequality dealing with monotone non-decreasing function, the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.FindingsIt turns out that the authors’ delay-dependent sufficient condition can be formed in terms of linear matrix inequalities conditions. Two examples show the effectiveness of the obtained results.Originality/valueThe novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem, chain rule and a novel integral inequality on monotone non-decreasing function.

Sign in / Sign up

Export Citation Format

Share Document