On the existence of stable asymmetric limit cycles and chaos in unforced symmetric relay feedback systems

We study the occurrence of bifurcations leading to the formation of asymmetric orbits and chaos in unforced relay feedback systems with a symmetric relay characteristic. Specifically, we show that novel bifurcation mechanisms cause the formation of stable periodic solutions with segments of sliding motion. We then characterise the formation of asymmetric stable periodic solutions and detail the route to chaos exhibited by a representative third-order example.