dynamical system
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A dynamical system is a mathematical model that describes how a point moves through space as time passes. It matters because it helps scientists and engineers predict and understand how real-world things change over time, from the orbits of planets to the spread of diseases.
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Article
A set of dynamical systems. Top left: a cellular automata. Top center: Exterior billiards. Top right a constrained 3-body problem. Bottom left a Poincare section of a Standard map (chaos arise in the dotted regions). Middle bottom: a chaotic Dynamical billiards (a symptom of chaos here are the trajectories filling the configuration space). Bottom right: A geodesic flow such as light on a surface, trajectories are geodesics i.e. minimum paths, in this case the phase space is a torus (stable orbits arise when the periods are rational, if irrational that is a path to chaos).
In mathematics, physics, engineering and systems theory, a dynamical system is the description of how a system evolves in time.