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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]
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.
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.
In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.
Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. [1] Algebraic geometry is one of the main areas of mathematical research supporting nonlinear algebra, while major components coming from computational mathematics support the development of the area into maturity.
In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects.
This is an example of a non-linear functional. The Riemann integral is a linear functional on the vector space of functions defined on [a, b] that are Riemann-integrable from a to b. In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author).
See Michaelis–Menten kinetics for details . 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.