Asymptotic stability refers to the property of a dynamical system where, after a disturbance, the system returns to a stable equilibrium point as time approaches infinity. In other words, not only does the solution converge to the equilibrium point, but it also does so in a way that ensures all nearby trajectories eventually follow this path back to stability. This concept is vital when analyzing systems of ordinary differential equations (ODEs) and understanding their long-term behavior in phase plane analysis.
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