分片线性逼近的动态特性分析

Dynamic behavior of piecewise-linear approximations

为了合理地应用分片线性逼近方法解决非线性动态系统问题,对非线性动态特性在分片线性逼近下的一致性问题展开研究。在对典型的混沌映射Logistic映射进行分片线性逼近时,分片线性系统会表现出一些不同于原系统的动态特性。即使在静态逼近精度很高的情况下,逼近所得的分片线性系统的分岔图与原系统的分岔图也会有很大的差异。分析表明分片线性系统与原系统光滑性的差异是导致动态特性差异的原因。继而使用光滑化的分片线性模型作逼近,逼近结果的动态特性能够保持与原系统一致。光滑化的分片线性模型适用于逼近非线性动态系统。

The use of piecewise-linear approximations to model nonlinear dynamic systems depends on the dynamic behavior of the piecewise-linear approximations.When the piecewise-linear approximation technique is used here to model the Logistic map,differences in the dynamic behavior are found between the approximation model and the original system.Even when the static error is very small,there are obvious differences between the bifurcation diagram of the original system and that of the piecewise-linear approximation.The piecewise-linear approximation is not as smooth as the original system,which causes the differences.A smoothed piecewise-linear model gives the same dynamic behavior as the original system,so smoothed piecewise-linear models are suitable for approximating nonlinear dynamic systems.