Dynamics of relay relaxation oscillators

Relaxation oscillators can usually be represented as a feedback system with hysteresis, The relay relaxation oscillator consists of relay hysteresis a nd a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators, In particular we give a complete analysis for the case of unimodal periodi c orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal o rbits, Finally, we focus on oscillators with an integrator as the linear co mponent, and study the entrainment under external forcing, and phase lockin g when such oscillators are coupled in a ring.