一类非线性离散动态系统的分析

时序电路是一类重要的离散动态系统,它在数学控制、计算机、数字通信等工程系统中应用得很普遍。线性时序电路理论已比较成熟。然而,由于非线性带来的本质困难,非线性时序电路理论的某些方面还相当薄弱。即使对一类结构简单的非线性时序电路——非线性移位寄存器,其状态图中圈数与圈长的分析计算仍缺乏系统的理论。而这类寄存器在数字控制、计算机、编译码器、密码机等工程系统中有重要的应用。

ANALYSIS OF A KIND OF NONLINEAR DISCRETE DYNAMIC SYSTEMS

Logical algebra is a kind of important quasi-field.This paper discusses the dynamicsystems over logical algebra,We give a formula for the number of cycles in a state graph forlinear systems which correspond to a kind of nonlinear systems over Galois field.Next we givea formula for the number of small cycles in a state graph for nonlinear systems.We may usethese results to analyse nonlinear sequential circuits and nonlinear shift-registers.