Broadly speaking, a dynamical system refers to any mathematical construct (for instance, a system of equations) in which there is some kind of "feedback effect." Examples of dynamical systems include linear and non-linear systems of differential equations (ordinary or partial), difference equations, and recurrence relations. Almost every technical field requires the consideration of dynamical systems - it is one of the cornerstones of modern applied mathematics. Famous examples of dynamical systems include the logistic equation and the Lorenz equations.
For the vast majority of dynamical systems, it is impossible to derive an exact solution, and so various approximation techniques have been developed.
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