Reasons for nonlinearity: globality and noncommutativity

A dynamic process modeled by ordinary differential equations is considered. If a nonautonomous system of ordinary differential equations has a general solution in a certain area, than the system can be simplified by nonautonomous substitution of variables: right parts turn to zeroes. Right parts of an autonomous system of ordinary differential equations in the neighborhood of nonsingular points can be linearized. A separable system where the right part contains linear combination of autonomous vector fields and factors are functions of independent variable is considered. If the fields commute than they can be linearized by general substitution of variables.