In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.

गतिकीय तन्त्र ऐसी प्रक्रिया या गणितीय मॉडल जिसमें निहित चरों का मान समय पर निर्भर करता है तथा जिसमें निम्नलिखित दो गुण होते हैं:

• कारण-कार्य (causal) : भविष्य की अवस्थाएँ केवल वर्तमान ए॰ं भूत अवस्थाओं के उपर निर्भर हों।

• निर्धर्णीय (डिटरमिनिस्टिक) : भविष्य के किसी भी क्षण पर चरों का मान ए॰ और केवल ए॰ हो।