Hyperchaos co-existing with periodic orbits in a frictional oscillator

Abstract

This work reports observations of complex dynamical behavior and chimera-alike dynamics in a self-excited frictional oscillator with a weak stiffness nonlinearity. Multi-stability in the form of several co-existing stable limit cycle solutions are identified for a wide range of system parameters. For a particular system configuration, an unstable periodic orbit is found that gives rise to irregular long-term behavior. Trajectories starting from this orbit turn out to be hyper-chaotic with multiple positive Lyapunov exponents. Trajectories starting from different regions in phase space converge to stable limit cycles. Hence, this numerical study reveals co-existing regular and irregular dynamics at a fixed system configuration. This sensitive dependence of the qualitative system dynamics on initial conditions adds new aspects to a better understanding of the rich dynamic behavior of structures subjected to friction-induced vibrations.