A dynamical system is a mathematical concept used to describe how a set of variables changes over time. In particular, it is a system where the state of the system at any given time determines its future behavior.
In a dynamical system, there is typically a set of rules or equations that determine how the state of the system changes in response to various inputs or stimuli. These rules may be deterministic, meaning that the future state of the system is entirely determined by its present state, or they may be probabilistic, allowing for some degree of randomness or uncertainty.
Examples of dynamical systems include physical systems like the motion of planets or the behavior of fluids, biological systems like the growth of populations or the spread of diseases, and economic systems like the fluctuations of stock prices or the behavior of markets. Dynamical systems can be modeled and analyzed using a variety of mathematical tools, including differential equations, chaos theory, and network theory.