Gui Zhanji, Ge Weigao
Department of Computer Science, Hainan Normal University, Haikou, HaiNan 571158, People's Republic of China.
Chaos. 2006 Sep;16(3):033116. doi: 10.1063/1.2225418.
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.
利用重合度理论中的连续定理并构造合适的Lyapunov函数，我们研究了具有脉冲的分流抑制细胞神经网络周期解的存在性、唯一性和全局指数稳定性，(\frac{dx_{ij}}{dt}=-a_{ij}x_{ij}-\sum_{(k,l)\in N_{r}(i,j)}C_{ij}(kl)f_{ij}[x_{kl}(t)]x_{ij}+L_{ij}(t),t > 0,t\neq t_{k};\Delta x_{ij}(t_{k})=x_{ij}(t_{k}^{+})-x_{ij}(t_{k}^{-})=I_{k}[x_{ij}(t_{k})],k = 1,2,\cdots)。此外，数值模拟表明我们的系统可以呈现多种复杂形式，包括周期振荡和混沌奇异吸引子。据我们所知，这些结果是首次获得。一些研究者已将脉冲引入他们的模型，但从未发现类似结果。
