Characteristics of coexisting attractors and ghost orbiting in an optomechanical microresonator

We explore the nonlinear interactions of an optomechanical microresonator driven by two external optical signals. Optical whispering-gallery waves are coupled to acoustic surface waves of a fused silica medium in the equatorial plane of a generic microresonator. The system exhibits coexisting attractors whose behaviors include limit cycles, steady states, tori, quasi-chaos, and fully developed chaos with ghost orbits of a known attractor. Bifurcation diagrams demonstrate the existence of self-similarity, periodic windows, and coexisting attractors and show high-density lines within chaos that suggests a potential ghost orbit. In addition, the Lyapunov spectral components as a function of control parameter illuminate the dynamic nature of attractors and periodic windows with symmetric and asymmetric formations, their domains of existence, their bifurcations, and other nonlinear effects. We show that the power-shift method can access accurately and efficiently attractors in the optomechanical system as it does in other nonlinear systems. To test whether the ghost orbit is the link between two attractors interrupted by chaos, we examine the elements of the bifurcation diagrams as a function of control parameter. We also use detuning as a second control parameter to avoid the chaotic region and clarify that the two attractors are one.