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In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
An example of a nonlinear delay differential equation; applications in number theory, distribution of primes, and control theory [5] [6] [7] Chrystal's equation: 1 + + + = Generalization of Clairaut's equation with a singular solution [8] Clairaut's equation: 1
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations (iterations).
See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations. A–F [ edit ]
Some special cases of nonlinear programming have specialized solution methods: If the objective function is concave (maximization problem), or convex (minimization problem) and the constraint set is convex , then the program is called convex and general methods from convex optimization can be used in most cases.
An example of a nonlinear control system is a thermostat-controlled heating system. A building heating system such as a furnace has a nonlinear response to changes in temperature; it is either "on" or "off", it does not have the fine control in response to temperature differences that a proportional (linear) device would have.
For nonlinear equations these questions are in general very hard: for example, the hardest part of Yau's solution of the Calabi conjecture was the proof of existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the Navier–Stokes equations is one of the seven Millennium Prize problems in ...
Nonlinear narrative, disjointed narrative, or disrupted narrative is a narrative technique where events are portrayed, for example, out of chronological order or in other ways where the narrative does not follow the direct causality pattern of the events featured, such as parallel distinctive plot lines, dream immersions or narrating another story inside the main plot-line.