ABSTRACT
In this talk I will discuss the dynamics of certain systems of interest in robotics and synthetic biology and consider in particular the existence of periodic behavior. I will discuss the existence or periodic orbits quite generally in certain hybrid and cyclic systems and discuss applications to bipedal locomotion, rolling systems with impacts and biological oscillators. The talk contains application of Poincare maps and bifurcation theory. Parts of these were done in collaboration with Will Clark and Matt Kvalheim.