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all natural systems are nonlinear time variant system, as these system are difficult to analyse mathematically, we will consider linear time invariant system bcoz they are easy to analyse and modelling these systems are also easy. for example if we want to construct a vocal system as human vocal system the system as to change with time and should consider the external agency, and realising these type of systems will be very very difficult.
They are modelled generally using the Volterra series, you can find some information on them on the web. But I think it would be better to get some Math book from a library and then study them.
Mathematically every system can be modeled linear or nonlinear. for nonlinear systems the relation between output and input or output and states are not linear. there are several way to simplify the nonlinear equations or find a more simple method to get the desired data. sometimes we use nonlinear state space equations, sometimes with some numerical method we find the solution and sometime with other methods such as voltera series and so on.
but if you mean how we can use laplace transform for nonlinear system this is the answer.
first by using linearization method we can linearize our nonliear system to a specific linear system whcih actually has same response in our specific range of working. then it is possible to apply Laplace Transform .
If we want to find more accurate solution we use numerical method to solve nonlinear equations.
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