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Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them.

Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them.

分岔理论是一个数学研究的变化，在定性或拓扑结构的一个给定的家庭，如积分曲线的一族向量场，和解决方案的一族微分方程。在动力系统的数学研究中，当系统的参数值(分岔参数)发生微小的平滑变化时，系统的行为就会发生突然的“定性”或拓扑变化。在连续系统(由常微分方程、常微分方程或偏微分方程描述)和离散系统(由映射描述)中都存在分岔。1885年，亨利 · 庞加莱在第一篇数学论文中首次提出了“分岔”这一概念，揭示了这种行为。亨利 · 庞加莱后来还对各种类型的静止点进行了命名和分类。

分岔理论是数学中研究给定族的定性或拓扑结构的改变，例如向量场中的积分曲线以及一族微分方程的解。分岔常用于动力系统的数学研究中，是指当系统的参数值(分岔参数)发生微小平滑的变化时，系统发生突然的“定性”或拓扑变化。分岔在连续系统(由常微分方程、微分方程或偏微分方程描述)和离散系统(由映射描述)中均存在。1885年，亨利 · 庞加莱首次在论文中提到“分岔”一词，这也是数学中揭示该行为的第一篇论文，后来亨利 · 庞加莱也对不同的驻点进行了命名和分类。