Lyapunov stability refers to the property of an equilibrium point in a dynamical system where nearby trajectories remain close to that equilibrium over time. This concept is crucial in determining how solutions behave when subjected to small perturbations, highlighting whether the system can return to equilibrium or diverge away from it. The analysis of Lyapunov stability often involves evaluating the behavior of the system's phase portraits and understanding the conditions under which stability can be guaranteed.
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