ABSTRACT
The linear stability analysis discussed in the previous chapter provides information about the onset of an instability and about its nature. It tells us which parameter can drive the instability, the threshold value at which the instability occurs, and the type of mode that grows at the instability point. Since the analysis addresses infinitesimally small perturbations about the state whose stability is studied, it does not provide information about the new state the system evolves toward. Indeed, the general solution of the system (5.58) of
linear ODEs describes exponentially growing perturbations which soon break the assumption of small perturbations.
