Education and Development BIFURCATIONS IN DYNAMICAL SYSTEMS
通过多个例子说明动态系统中的分岔概念，提出分岔动态系统框架作为突变理论模型的替代，并用股市模型演示该方法。
Abstract The concept of bifurcation in a dynamical system is illustrated through several examples. The elementary catastrophes are equilibrium sets of specific kinds of dynamical systems. The framework of bifurcating dynamical systems is put forward as an alternative to catastrophe theory models. Dynamical systems models require explicit accounting of all their underlying hypotheses. They offer unambiguous answers in return. The fuzzy transition from hypotheses to results so characteristic of the catastrophe theory literature is absent. The method is illustrated using a stock‐market model.