Stability of periodic solutions

Abstract

Periodic solutions of a differential equation are time-dependent or space-dependent orbits, cycles, or oscillations. In this chapter a major concern is time-dependent periodicity (“time periodicity” for short) of solutions of autonomous systems of ODEs For time-periodic solutions, there is a minimum time interval T > 0 (the “period”) after which the system returns to its original state: for all t. In Section 7.7 we turn our attention to the non-autonomous case.