- "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."
The study of non-linear phenomena in systems, including chaos theory and nonlinear differential equations.
- "Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature."
- "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."
- "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)."
- "some interesting phenomena such as solitons, chaos, and singularities are hidden by linearization."
- "it is in fact not random" and "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."
- "Some authors use the term nonlinear science for the study of nonlinear systems."
- "This term is disputed by others: Using a term like nonlinear science is like referring to the bulk of zoology as the study of non-elephant animals."
- "engineers"
- "chaotic, unpredictable, or counterintuitive"
- "by a nonlinear system of equations"
- "solitons, chaos, and singularities"
- "This works well up to some accuracy and some range for the input values"
- "such chaotic behavior may resemble random behavior, it is in fact not random"
- "biologists, physicists, mathematicians, and many other scientists"
- "some aspects of the dynamic behavior of a nonlinear system can appear to be counterintuitive, unpredictable or even chaotic"
- "but some interesting phenomena such as solitons, chaos, and singularities are hidden by linearization."