Due to nonlinearity, we can not apply the superposition
principle(linearity and homogeneity) as a result all the linear
mathematical tools like Laplace transform, Fourier transform,z
transform, Bode plot, root locus and Nyquist stability criteria
fails.
so analysis of the non-linear system is rigorous, complex, less
general, often applying to only narrow categories system. These
include limit cycle theory, Poincaré maps, Lyapunov stability
theory, and describing functions.
Nonlinear systems are often analyzed using numerical methods on
computers.