Perturbatis

Perturbatis is a theoretical perturbation parameter used in mathematical modeling and theoretical analyses to quantify the impact of small disturbances on a baseline system. The term combines perturbation with a suffix -atis and is used mainly in educational and exploratory contexts to illustrate how slight changes propagate through a model.

Definition and formalism: If a system state or quantity F depends on a control parameter ε, perturbatis designates ε as a small, dimensionless perturbation parameter. One often expands F(ε) in a perturbative series F(ε) = F0 + εF1 + ε^2F2 + ... with higher-order terms neglected when |ε| is sufficiently small.

Examples: In a dynamical system dx/dt = A x, a perturbatis perturbation modifies the system matrix to A + εΔA, yielding a perturbed solution that can be analyzed with standard perturbation theory. In an input-output model y = C x, the added term ε δy represents the perturbatis contribution to the output.

Applications and scope: Perturbatis is used primarily as a pedagogical tool across physics, engineering, climate science, and economics to demonstrate how small changes can propagate, as well as to develop sensitivity analyses and stability assessments. It does not denote a single physical quantity and is not a universally standardized term.

Limitations: The approach assumes small ε and smooth dependence; for large disturbances or highly nonlinear systems, perturbatis expansions may fail or require resummation or numerical methods.

See also: Perturbation theory, Sensitivity analysis, Linearization, Asymptotic analysis.