A dynamical system is an interactive nonlinear system that evolves over time, showing transformations of behavior and an increase in complexity. Key to this evolution is the presence and emergence of attractors, most notably chaotic attractors. The changes in the system's organization and behavior are known as bifurcations.

Dynamical systems are deterministic systems, although they can be influenced by random events. Times series data of dynamical systems can be graphed as phase portraits in phase space in order to indicate the qualitative or topological properties of the system and its attractor(s). For example, various physiological systems, such as the heart, can be conceptualized as dynamical systems. Seeing physiological systems as dynamical systems opens up the possibility of studying various attractor regimes. Moreover, certain diseases can be understood now as "dynamical diseases," meaning that their temporal phasing can be a key to understanding pathological conditions.