🌀
Fixed Points and Stability
★★★★☆Undergraduate
📖Definition
A fixed point is a state that doesn't change over time in a dynamical system. Fixed points can be stable (attractors), unstable, or saddle points.
📐Formulas
f(x^*) = x^* (discrete), f(x^*) = 0 (continuous)
Fixed point condition
|f'(x^*)| < 1 : stable, |f'(x^*)| > 1 : unstable
Stability in discrete systems
✏️Examples
예제 1
Analyze fixed points and stability of f(x) = x² - x - 1.
⚡Applications
Control Theory
System stabilization
Ecology
Equilibrium populations
Economics
Market equilibrium
🔗Related Documents
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