title: On the periodic dynamics of a class of time-varying delayed neural networks via differential inclusions.
abstract: 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.
authors.affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China. caizuowei01@126.com
authors.forename: Zuowei
authors.initials: Z
authors.lastname: Cai
authors.forename: Lihong
authors.initials: L
authors.lastname: Huang
authors.forename: Zhenyuan
authors.initials: Z
authors.lastname: Guo
authors.forename: Xiaoyan
authors.initials: X
authors.lastname: Chen
mesh_terms: D016571:Neural Networks, Computer; D010507:Periodicity; D013997:Time Factors