动态系统理论是数学领域中的一部份．主要在描述复杂的动态系统，一般会用微分方程或差分方程来表示。若用微分方程来表示，会称为「连续动态系统」，若用差分方程来表示，则称为「离散动态系统」。若其时间只在一些特定区域连续，在其余区域离散，或时间是任意的时间集合（像康托尔集），需要用时标微积分来处理。有时也会需要用混合的算子来处理，像微分差分方程。

动态系统理论处理动态系统长期的量化特性．及研究一些自然界基本的运动方程系统的解，包括卫星的运动方程，电路的特性．以及生物学中出现偏微分方程的解。许多当代的研究集中在混沌理论的研究。

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a cantor set—one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.