In particular, a differential equation is linear if it is linear in terms of the unknown function and its derivatives, even if nonlinear in terms of the other variables appearing in it.Īs nonlinear dynamical equations are difficult to solve, nonlinear systems are commonly approximated by linear equations ( linearization). Systems can be defined as nonlinear, regardless of whether known linear functions appear in the equations. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the unknown variables or functions that appear in them. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. For other uses, see Nonlinearity (disambiguation). For video and film editing, see Non-linear editing system. This article is about "nonlinearity" in mathematics, physics and other sciences.
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