Stability theory studies the response of a dynamical system to small changes of its state. Linear stability of a planar equilibrium describes the response near equilibria using the linearized evolution.
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Stability theory is a branch of mathematics and systems theory that deals with the stability of solutions to dynamic systems, particularly in the context of differential equations and control theory. The central question in stability theory is whether small perturbations or changes in the initial conditions of a system will lead to small changes in its future behavior.