Coupled

Coupled is an adjective used to describe two or more components whose states or dynamics influence one another. When components are coupled, a change in one component can propagate to others, and the behavior of the whole system cannot be understood by studying parts in isolation. The process or interaction that links them is called coupling; conversely, decoupling is the separation of the components to reduce influence.

In physics and engineering, coupling appears in many forms: mechanical, electrical, thermal, or quantum. Examples include coupled oscillators, where two pendulums exchange energy through a connecting link; and electrical circuits with mutual inductance or capacitive coupling. The strength of coupling governs energy transfer and collective modes, such as normal modes in a system of coupled oscillators or the eigenmodes of a coupled differential equation system.

In mathematics and control theory, coupled models are described by sets of interdependent equations. Coupled differential equations require simultaneous solution; the coupling terms act as inputs from one equation to another. Decoupling techniques, coordinate transformations, or symmetry considerations aim to simplify analysis. In control, coupling between subsystems affects stability and performance, leading to multi-input, multi-output design considerations.

In science and technology, coupling concepts appear in biology, chemistry, climate science, and economics. Examples include coupled biochemical networks, gene regulation with feedback, and coupled climate models that exchange information between atmosphere and ocean components. Across domains, understanding coupling helps describe how complex systems generate coordinated behavior from interacting parts.