title: Periodic solution for state-dependent impulsive shunting inhibitory CNNs with time-varying delays.
abstract: In this paper, we consider existence and global exponential stability of periodic solution for state-dependent impulsive shunting inhibitory cellular neural networks with time-varying delays. By means of B-equivalence method, we reduce these state-dependent impulsive neural networks system to an equivalent fix time impulsive neural networks system. Further, by using Mawhin's continuation theorem of coincide degree theory and employing a suitable Lyapunov function some new sufficient conditions for existence and global exponential stability of periodic solution are obtained. Previous results are improved and extended. Finally, we give an illustrative example with numerical simulations to demonstrate the effectiveness of our theoretical results.
authors.affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey. Electronic address: msayli@metu.edu.tr.
authors.forename: Mustafa
authors.initials: M
authors.lastname: Şaylı
authors.affiliation: Gazi University, Polatlı Faculty of Science and Arts, Department of Mathematics, 06900 Ankara, Turkey; Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey. Electronic address: enesyilmaztr@gmail.com.
authors.forename: Enes
authors.initials: E
authors.lastname: Yılmaz
mesh_terms: D006801:Humans; D009433:Neural Inhibition; D016571:Neural Networks, Computer; D010507:Periodicity; D013997:Time Factors
keywords: Global exponential stability; Periodicity; Shunting inhibitory cellular neural networks; State-dependent impulsive systems