 In mathematics and science, the non-linear system is a system in which the change of the output is not proportional to the change of the input. Non-linear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently non-linear in nature. The linear 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 non-linear system is described in mathematics by a non-linear system of equations, which is a set of simultaneous equations in which the unknowns are the 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 non-linear system of equations, the equation has 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 non-linear, 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 non-linear in terms of the other variables appearing in it. As non-linear dynamical equations are difficult to solve, non-linear 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 sleetons, chaos, and singularities are hidden by linearization. It follows that some aspects of the dynamic behavior of the non-linear 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 non-linearity is one of the reasons why accurate long-term forecasts are impossible with current technology.