非平常的动力系统分岔分析是我最近在查询Floquet理论的应用时找到的，浏览了这篇的introduction部分后，知道这个方面的工作虽然“The dynamics of non-smooth systems is a relatively young research field”，但也有不短的研究历史和不少的研究文献了。

我关心的是这些不同于平滑系统的分岔特点，对于斑图的演化会有什么样的影响。这也是我最近在做的一个工作。但原来并不是以non-smooth为卖点，只是在分析的时候发现在方程中对某一项取绝对值后，这个系统再应用Jacobian矩阵来分析时要将原来的分析方法推广一下才可以。但是这种推广我没有进一步去证明是可行的意图，所以也就找文献，幸运的是有人做过了。

其实很多斑图研究的文献里常用的FHN模型的变体Bar模型，Chuas'模型都是非光滑的。但有可能它们的分岔特点与平滑系统相近，所以我还没有见到有什么文献专门讨论Bar模型的分岔特征与常见动力系统的不同。

European Journal of Mechanics A/Solids 25 (2006) 595–616

Abstract
The aim of the paper is to give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems.A small number of well-chosen examples of various kinds of non-smooth systems will be presented, followed by a discussion of the bifurcation phenomena in hand and a brief introduction to the mathematical tools which have been developed to study these phenomena. The bifurcations of equilibria in two planar non-smooth continuous systems are analysed by using a generalised Jacobian matrix. A mechanical example of a non-autonomous Filippov system, belonging to the class of differential inclusions, is studied and shows a number of remarkable discontinuous bifurcations of periodic solutions. A generalisation of the Floquet theory is introduced which explains bifurcation phenomena in differential inclusions. Lastly, the dynamics of the Woodpecker Toy is analysed with a one-dimensional Poincaré map method. The dynamics is greatly influenced by simultaneous  impacts which cause discontinuous bifurcations.