Chaos in three coupled rotators: From Anosov dynamics to hyperbolic attractors

Abstract

Starting from Anosov chaotic dynamics of geodesic flow on a surface of negative curvature, we develop and consider a number of self-oscillatory systems including those with hinged mechanical coupling of three rotators and a system of rotators interacting through a potential function. These results are used to design an electronic circuit for generation of rough (structurally stable) chaos. Results of numerical integration of the model equations of different degree of accuracy are presented and discussed. Also, circuit simulation of the electronic generator is provided using the NI Multisim environment. Portraits of attractors, waveforms of generated oscillations, Lyapunov exponents, and spectra are considered and found to be in good correspondence for the dynamics on the attractive sets of the self-oscillatory systems and for the original Anosov geodesic flow. The hyperbolic nature of the dynamics is tested numerically using a criterion based on statistics of angles of intersection of stable and unstable subspaces of the perturbation vectors at a reference phase trajectory on the attractor.