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Introduction to Nonlinear system

A Nonlinear system, in mathematics, is one which does not satisfy the super position principle or one whose output is not directly proportional to its input; a linear system fulfills such conditions or a nonlinear system is any problem where the variable(s) to be solved cannot be written as a linear combination of self-governing components. The non-homogeneous system that is linear, separate from the presence of a function of the independent variables is non-linear according to a definition; however such systems are usually studied alongside linear systems as they can be transformed to a linear system of multiple variables.

Nonlinear problems are of interest to engineers, physicists, and mathematicians as most physical systems are inherently nonlinear in nature. The non-linear equations are not easy to solve and give rise to the interesting phenomena like chaos. A few aspects of the weather (though not the climate) are seen to be chaotic, where minor changes in one section of the system produce complex effects throughout. The non-linear system is not arbitrary.

**Types of nonlinear behaviors**

- Indeterminism - The behavior of this kind of system cannot be predicted.
- Multistability - This behavior irregular between two or more exclusive states.
- Aperiodic oscillations - functions which do not repeat values after some period (or else termed as chaotic oscillations or chaos).
- Amplitude death- any oscillations present in the system cease since of some kind of interaction with the other system or feedback by similar system.

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