Stability and instability for periodic solutions of delay equations with "steplike" feedback

Abstract

We consider the stability of periodic solutions of certain delay equations $x'(t) = f(x_t)$ for which the special structure of the equation allows us to define return maps that are semiconjugate to finite-dimensional maps. We present some general results on assessing stability with the aid of such a semiconjugacy. We then apply our general results to exhibit a stable periodic solution of an equation with two fixed delays and an unstable periodic solution of an equation with state-dependent delay.

Keywords

• stability of periodic solutions