It is now a truism that nonlinearity is everywhere around us. But what is nonlinearity? We know of linearity through Ohm's law, which essentially shows a linear dependence between physical parameters. Let us take a look at a clock pendulum, in which the period of oscillation does not depend in any way on the amplitude, provided we move close to the point of equilibrium. But if the pendulum is swung with greater amplitude, the period of oscillation becomes dependent on the amplitude. It looks that large amplitude brings into play a new physical reality, which doesn't manifest itself at small amplitudes, and, in fact, which now becomes predominant. We say that here we have nonlinear waves that move with large and often, very large amplitudes. If we now delve into the past, we meet several linear relationships. It is only during the past few decades that scientists have started grappling with something different from linearities and we agree to call them nonlinearities. Nonlinear science is a recent and premature coinage. We often use the terms “nonlinear system” or often “nonlinear dynamics”. The emerging field of mathematical sciences, not to be looked upon as a menagerie of nonlinearities, provides in its variety of components e.g. physical sciences, life sciences, ecological sciences, social sciences etc, different contemporary phases of nonlinear science or nonlinear dynamics or nonlinear systems.

The origin of pursuits on nonlinearities dates back to the later part of the nineteenth century.