investigating the linear stability solution of an equation is equivalent to finding the spectrum of the linearized equation around that solution. If the spectrum lies in the left complex half plane then it is stable. Bifurcation theory basically discusses what happens when the spectrum of given a solution intersects the vertical axis, i.e. when a solution “is about to lose stability”. For instance, if there is a curve of solutions along which one eigenvalue (which is a particular element of the spectrum) crosses the vertical axis in the origin then NEW solutions arise. This may be kept in mind as a principle: If the linear stability properties change along a family of solutions, then new solutions are born. As a consequence, linear stability analysis is used in bifurcation theory in order to prove the existence of new solutions.

Yours, Rainer

]]>If stability analysis can b done by other techniques then why should we prefer bifurcation analysis? ]]>

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