Linear stability analysis classifies a hyperbolic equilibrium from the eigenvalues of the vector field's Jacobian.
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Linear stability refers to the analysis of the stability of equilibrium points (also known as steady states or fixed points) in dynamical systems by examining the behavior of small perturbations around those points. It is a fundamental concept in various fields such as physics, engineering, biology, and economics. When considering a dynamical system described by equations (often ordinary differential equations), the stability of an equilibrium point can be assessed by performing a linearization of the system.