What does nonlinear system mean?
Definitions for nonlinear system
non·lin·ear sys·tem
This dictionary definitions page includes all the possible meanings, example usage and translations of the word nonlinear system.
Princeton's WordNet
nonlinear systemnoun
a system whose performance cannot be described by equations of the first degree
Wikipedia
Nonlinear system
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. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. 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. 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. Systems can be defined as nonlinear, regardless of whether known linear functions appear in the equations. 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. As nonlinear dynamical equations are difficult to solve, nonlinear systems are commonly approximated by linear equations (linearization). This works well up to some accuracy and some range for the input values, but some interesting phenomena such as solitons, chaos, and singularities are hidden by linearization. It follows that some aspects of the dynamic behavior of a nonlinear system can appear to be counterintuitive, unpredictable or even chaotic. Although such chaotic behavior may resemble random behavior, it is in fact not random. For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. This nonlinearity is one of the reasons why accurate long-term forecasts are impossible with current technology.
ChatGPT
nonlinear system
A nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear system can specifically refer to a system of equations in which the unknowns 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. In other words, it is a system where the variables are not just simply added together or multiplied by constant coefficients, but are rather squared, cubed, or raised to other powers. It is characterized by complex, unpredictable behavior.
Wikidata
Nonlinear system
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 equation to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it. It does not matter if nonlinear known functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the undefined function and its derivatives, even if nonlinear in terms of the other variables appearing in it. 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 are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. A nonlinear system is not random.
Matched Categories
Numerology
Chaldean Numerology
The numerical value of nonlinear system in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of nonlinear system in Pythagorean Numerology is: 5
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"nonlinear system." Definitions.net. STANDS4 LLC, 2024. Web. 17 Jun 2024. <https://www.definitions.net/definition/nonlinear+system>.
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