Definition
Mathematical models that describe how a system's state changes over time according to fixed rules.
Detailed Explanation
Dynamical Systems theory studies systems that evolve over time according to mathematical rules. It encompasses both continuous and discrete time systems linear and nonlinear behaviors and deterministic and stochastic elements. The approach uses differential equations difference equations and state space representations to analyze system behavior stability and long-term evolution patterns.
Use Cases
Climate system modeling population dynamics analysis economic system behavior prediction mechanical system design and chemical reaction kinetics modeling.