Across mathematics, physics, biology, and ecology, the concept of stability provides a unified framework for understanding how dynamic systems maintain order, resist disruption, or undergo radical transformations.

Mathematical Foundations In dynamical systems, stability is understood through fixed points (equilibrium states). A system at a fixed point remains there unless disturbed. Stable fixed points (attractors) pull perturbed systems back to equilibrium, while unstable fixed points (repellers) push them away. When system parameters change, they can cross a bifurcation (or tipping point)—a threshold where the system undergoes a sudden, qualitative change in behavior, such as transitioning from a stable to an unstable state.

Feedback Loops Stability is heavily governed by feedback. Negative feedback acts as a stabilizer by opposing  ...