5个态变量1个端口的细胞神经网络局部活动性理论

Some Analytical Criteria for Local Activity of One-port CNN with Five State Variables

局部活动性原理自Chua于1997年提出后,为研究耦合细胞出现复杂现象的起因提供了有力的工具,也为预测和判定某一类局部耦合非线性系统(反应扩散细胞神经网络系统)能否展示震荡或混沌等复杂的动力学行为提供了新的必要性的判据。在实际运用中,局部活动原理只提供了一个形式的判别框架,需要针对扩散反应CNN方程"态变量"和"端口"的个数建立相应的解析判别法。本文建立了5个态变量1个端口的反应扩散细胞神经网络方程的局部活动性理论的解析判别法,并给出了相应的判别法的4个定理的证明。通过这4个定理,可以对某类具有5个变量的非线性系统的复杂性进行分析和判断。

The local activity principle of the Cellular Nonlinear Networks(CNN) introduced by Chua has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice formed by coupled cells.This paper presents some analytical criteria for local activity principle in reaction-diffusion CNN cells that have one-port with five state variables.The analytical criteria consist of four Theorems.The Theorems provide the inequalities of the parameters of the CNN with five state variables and one-port.The inequalities can be used for calculating the bifurcation diagram of the corresponding CNN to determine emergence of complex dynamic patterns of the CNN.