In mathematics, a nonlinear system is one that does not satisfy the superposition principle, or one whose output is not directly proportional to its input; a linear system fulfills these conditions. In other words, a nonlinear system is any problem where the variable(s) to be solved for cannot be written as a linear combination of independent components. A nonhomogeneous system, which is linear apart from the presence of a function of the independent variables, is nonlinear according to a strict definition, but such systems are usually studied alongside linear systems, because they can be transformed to a linear system of multiple variables.
Nonlinear problems are of interest to engineers, physicists and mathematicians because most physical systems are inherently nonlinear in nature. Nonlinear equations are difficult to solve and give rise to interesting phenomena such as chaos. Some aspects of the weather (although not the climate) are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. A nonlinear system is not random.
Read more about Nonlinear System: Definition, Nonlinear Algebraic Equations, Nonlinear Recurrence Relations, Nonlinear Differential Equations, Types of Nonlinear Behaviors, Examples of Nonlinear Equations, Software For Solving Nonlinear System
Famous quotes containing the word system:
“For the universe has three children, born at one time, which reappear, under different names, in every system of thought, whether they be called cause, operation, and effect; or, more poetically, Jove, Pluto, Neptune; or, theologically, the Father, the Spirit, and the Son; but which we will call here, the Knower, the Doer, and the Sayer. These stand respectively for the love of truth, for the love of good, and for the love of beauty.”
—Ralph Waldo Emerson (1803–1882)