perturbed

Perturbed is the past participle of perturb and is used as an adjective to describe something that has been disturbed, altered, or disrupted by an external influence. In everyday language it can imply agitation or unease, as in a perturbed state or schedule. In scientific contexts, perturbed denotes a system, equation, or dataset that has been modified by a perturbation, often a small or controlled change.

In mathematics, physics, and engineering, perturbation theory is a set of methods for approximating solutions to problems that are close to solvable ones by expanding in a small perturbation parameter. The idea is to understand how a slight modification to a problem affects its solutions, such as shifts in eigenvalues and eigenvectors when a linear operator is slightly altered. Perturbed equations and models describe how real-world influences alter idealized behavior.

Examples of perturbed systems appear in many fields. In celestial mechanics, an orbit is perturbed by the gravitational pull of other bodies. In climate science and engineering, external forces can perturb a system away from equilibrium. In data science and statistics, perturbations—such as added noise—are used for privacy, robustness, or simulation. In optimization, perturbed objectives or constraints help test stability and sensitivity of solutions.

Overall, perturbed conveys that a change or disturbance has altered the original state, often in a way that is analyzed to understand the system’s response.