Linearnonlinear

Linearnonlinear is a term used to describe models and systems that combine linear and nonlinear elements or behaviors. The concept emphasizes a hybrid structure where a linear component is paired with nonlinear processing, or where a system acts in a linear fashion within certain operating ranges and nonlinearly in others. While not a single formal theory, linearnonlinear appears in discussions of modeling, analysis, and design across engineering and science.

Common patterns associated with linearnonlinear models include linear time-invariant cores followed by nonlinear processing, linear filters coupled to static nonlinearities, and piecewise linear approximations that switch between linear regimes. In neuroscience, for example, linear-nonlinear-Poisson models encapsulate a linear filter fed into a nonlinear activation. In control and signal processing, systems may exhibit linear dynamics up to saturation or dead zones, with nonlinear effects becoming prominent beyond those regions.

Applications span communications, robotics, neuroscience, economics, and materials science, wherever both proportional, additive effects and nonlinear distortions influence behavior. Estimation and identification of linearnonlinear models often rely on separating the linear and nonlinear components, using linearization around an operating point, or employing block-structured identification methods that fit linear and nonlinear parts jointly. Challenges include identifiability, model order selection, and capturing strong nonlinearities without sacrificing interpretability. Overall, linearnonlinear describes a pragmatic approach to modeling real-world systems that cannot be adequately represented by purely linear or purely nonlinear formalisms.