Nonlinear system

A system of equations or transformations in which at least one relation is nonlinear. Its outputs need not scale proportionally with inputs, and its behavior can include multiple solutions or complex dynamics.

Superposition principle: A property in which combined inputs produce the sum of their separate outputs. Its failure is a defining feature of nonlinear systems.
Nonlinear equation: An equation in which the unknowns do not appear only in linear combinations. A nonlinear equation is the basic relation that can make a system nonlinear.
Predator–prey model: A mathematical model of interacting predator and prey populations over time. Its nonlinear interaction terms produce changing population cycles.
Linear system: A system whose equations or transformations preserve addition and scalar multiplication. It obeys superposition, unlike a genuinely nonlinear system.
Fixed point: A value that a function or transformation leaves unchanged. Fixed points identify steady states of nonlinear transformations.
Ordinary differential equation: An equation relating a function of one variable to its derivatives. Many nonlinear systems describe time evolution through coupled ordinary differential equations.
Navier–Stokes equations: Partial differential equations describing the motion of viscous fluids. Their nonlinear advection term couples fluid velocity to its own spatial variation.
Linear programming: An optimization method for a linear objective subject to linear constraints. Its linear structure enables guarantees and algorithms unavailable for general nonlinear optimization.
Bifurcation theory: The study of qualitative changes in a system's behavior as parameters vary. Changing a parameter can create or destroy equilibria and cycles.
Partial differential equation: An equation relating a function of several variables to its partial derivatives. Nonlinear partial differential equations model spatially extended systems.

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