nonlin

Nonlin is a shorthand often used to refer to nonlinearity or nonlinear systems. It is not a single object but a broad concept used across mathematics, physics, engineering, and data analysis. In practice, nonlinearity describes relationships or systems that cannot be described by a linear equation or obey the principle of superposition.

In mathematics, a linear relationship satisfies additivity and homogeneity; nonlinear means at least one of these properties fails. Common nonlinear forms include polynomial expressions with degree greater than one, exponential, logarithmic, or trigonometric functions. Nonlinear equations may have multiple solutions, no closed form, and can produce complex behavior such as curves that bend, self-intersect, or exhibit sensitivity to initial conditions.

In science and engineering, nonlinear dynamics can lead to phenomena such as chaos, bifurcations, and pattern formation. Examples include fluid flow described by the nonlinear convective term in the Navier–Stokes equations, nonlinear optics, and nonlinear electrical circuits. Many real-world systems exhibit nonlinearity, requiring specialized mathematical and numerical methods for analysis and simulation.

Analysis and modeling of nonlinearity often rely on linearization, perturbation methods, and numerical iterative techniques such as Newton-Raphson or related methods. In statistics and data science, nonlinear regression and nonlinear optimization are used to fit models that capture curvature and interactions that linear models miss.

The term nonlin is also used informally in software and documentation to denote nonlinear options, models, or functions. See also nonlinear, linearity, chaos theory.