Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

摘要

Dynamical equations are formulated and a numerical study is provided forself-oscillatory model systems based on the triple linkage hinge mechanism ofThurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomicmechanical constraint of three rotators as well as systems, where threerotators interact by potential forces. We present and discuss some quantitativecharacteristics of the chaotic regimes (Lyapunov exponents, power spectrum).Chaotic dynamics of the models we consider are associated with hyperbolicattractors, at least, at relatively small supercriticality of theself-oscillating modes; that follows from numerical analysis of thedistribution for angles of intersection of stable and unstable manifolds ofphase trajectories on the attractors. In systems based on rotators withinteracting potential the hyperbolicity is violated starting from a certainlevel of excitation.