If the dynamical system is then the linearization is the dynamical system, where is the derivative of evaluated at a solution.
A process of reduction to linear form by appropriate change of variables or by approximation. For example, 1) the equation = Ae bx becomes = + bx by the transformation = log ; = log ; or 2) the function exp() can be approximated by the linear Taylor polynomial for small .
Linearization in mathematics and its applications in general refers to finding the linear approximation to a function at a given point. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations. This method is used in fields such as engineering, physics, economics, and ecology.