Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses.
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(ij)dt=-a(ij)x(ij)- summation operator(C(kl)inN(r)(i,j))C(ij) (kl)f(ij)[x(kl)(t)]x(ij)+L(ij)(t), t>0,t not equal t(k); Deltax(ij)(t(k))=x(ij)(t(k) (+))-x(ij)(t(k) (-))=I(k)[x(ij)(t(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.
Gui
Zhanji
Z
Department of Computer Science, Hainan Normal University, Haikou, HaiNan 571158, People's Republic of China. zhanjigui@sohu.com
Ge
Weigao
W
D000465:Algorithms; D000818:Animals; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D017711:Nonlinear Dynamics; D009991:Oscillometry; D012815:Signal Processing, Computer-Assisted