Nonlinear system
In physics and other sciences, a
nonlinear system, in contrast to a linear system, is a system which does not satisfy the superposition principle – meaning that the output of a nonlinear system is not directly proportional to the input. In mathematics, a
nonlinear system of equations is a set of simultaneous equations in which the unknowns 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 nonlinear system of equations, the equation to be solved cannot be written as a linear combination of the unknown variables or functions that appear in it. It does not matter if nonlinear known 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. Typically, the behavior of a
nonlinear system is described by a
nonlinear system of equations.