Dynamical systems theory

Dynamical systems theory is a field of applied mathematics. It tries to describe complex dynamical systems, often using differential equations and difference equations. When differential equations are used, the theory is called "continuous" dynamical systems theory. When difference equations are used, it is called "discrete" dynamical systems theory.
The theory looks at the long-term behaviour of dynamical systems. It also studies solutions to the equations of motion, mainly for mechanical systems. The study also includes the motion of planets, or electronic circuits. Part of it focuses on solving Partial differential equations that occur in biology.