stability

Stability is a property of a system describing its tendency to resist perturbations or to return to an equilibrium state after disturbance. It can refer to a static notion, where the state remains constant in time, or to a dynamic notion, where the system evolves toward and potentially settles at an equilibrium. Stability is often contrasted with fragility or instability, where small disturbances lead to large changes.

In mathematics and dynamical systems, stability is formalized with definitions such as Lyapunov stability, where solutions starting near an equilibrium stay near it for all future times; asymptotic stability, where they also converge to the equilibrium as time goes to infinity; and exponential stability, with a specific rate of convergence. Energy methods and invariants are common tools for proving stability.

In physics and engineering, stability describes an object's balance, a structure's response to loading, or a control system's behavior under feedback. Structural stability concerns durability under varying loads; buckling represents a loss of stability. In control theory, bounded-input, bounded-output stability ensures that bounded inputs produce bounded outputs; margin measures quantify how close a system is to instability.

In economics and ecology, stability refers to persistence and predictability of variables like prices, growth, or populations in the face of shocks. Financial and macroeconomic stability aim to minimize volatility. Ecological stability involves resilience and resistance of ecosystems to disturbances, and their ability to recover after perturbations.

Stability is often balanced against other goals such as flexibility or performance. Its assessment depends on the time horizon, perturbation type, and the system's structure.