On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions

• Published in: Neural networks Vol. 33; pp. 97 - 113
• Main Authors: Cai, Zuowei, Huang, Lihong, Guo, Zhenyuan, Chen, Xiaoyan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2012; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Connectionism. Neural networks; Convergence in finite time; Discontinuous neuron activation; Exact sciences and technology; Global exponential stability; Neural Networks (Computer); Periodic solution; Periodicity; Time Factors; Time-varying delayed neural networks; Topological degree theory; Discontinuous neuron activation; Convergence in finite time; Global exponential stability; Time-varying delayed neural networks; Topological degree theory; Periodic solution; Autonomous system; Lyapunov method; Set computation; Dynamical system; Exponential stability; Degree theory; Modeling; Time varying system; Efficiency; Delay time; Discontinuity; Finite state machine; Interconnected power system; Delay system; Neural network; Topology; Equilibrium point; Activation function; Differential inclusion; Monotonicity; Lyapunov function
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2012.04.009

This paper investigates the periodic dynamics of a general class of time-varying delayed neural networks with discontinuous right-hand sides. By employing the topological degree theory in set-valued analysis, differential inclusions theory and Lyapunov-like approach, we perform a thorough analysis of the existence, uniqueness and global exponential stability of the periodic solution for the neural networks. Especially, some sufficient conditions are derived to guarantee the existence, uniqueness and global exponential stability of the equilibrium point for the autonomous systems corresponding to the non-autonomous neural networks. Furthermore, the global convergence of the output and the convergence in finite time of the state are also discussed. Without assuming the boundedness or monotonicity of the discontinuous neuron activation functions, the obtained results improve and extend previous works on discontinuous or continuous neural network dynamical systems. Finally, two numerical examples are provided to show the applicability and effectiveness of our main results.