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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]
A nonlinear system is defined as any system that is not linear, that is any system that does not satisfy the superposition principle. This negative definition tends to obscure that there are very many different types of nonlinear systems.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing , and telecommunications .
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light.
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function.
Linear vs. nonlinear. If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. A model is considered to be nonlinear otherwise. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them.
Linear optics is a sub-field of optics, consisting of linear systems, and is the opposite of nonlinear optics. Linear optics includes most applications of lenses, mirrors, waveplates, diffraction gratings, and many other common optical components and systems. If an optical system is linear, it has the following properties (among others):
Even if the plant is linear, a nonlinear controller can often have attractive features such as simpler implementation, faster speed, more accuracy, or reduced control energy, which justify the more difficult design procedure. An example of a nonlinear control system is a thermostat-controlled heating system. A building heating system such as a ...