Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses
- Department of Computer Science, Hainan Normal University, Haikou, HaiNan 571158 (China) and Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081 (China)
By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness, and global exponential stability of periodic solution for shunting inhibitory cellular neural networks with impulses, dx{sub ij}/dt=-a{sub ij}x{sub ij}-{sigma}{sub C{sub K}{sub 1}}{sub (set-membershipsign)=N{sub r}{sub (i,j)}C{sub ij}{sup kl}f{sub ij}[x{sub kl}(t)]x{sub ij}+L{sub ij}(t), t>0,t{ne}t{sub k}; {delta}x{sub ij}(t{sub k})=x{sub ij}(t{sub k}{sup +})-x{sub ij}(t{sub k}{sup -})=I{sub k}[x{sub ij}(t{sub k})], k=1,2,... . Furthermore, the numerical simulation shows that our system can occur in many forms of complexities, including periodic oscillation and chaotic strange attractor. To the best of our knowledge, these results have been obtained for the first time. Some researchers have introduced impulses into their models, but analogous results have never been found.
- OSTI ID:
- 20849475
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 16, Issue 3; Other Information: DOI: 10.1063/1.2225418; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
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