2015/10/13 by Sergey P. Kuznetsov · 7 citations
Physics and Astronomy · #CHAOS (operating system) #Chaos control and synchronization #Chaotic #Constraint (computer-aided design) #Intersection (aeronautics) #Linkage (software) #Phase (matter) #Quantum chaos and dynamical systems #Slow manifold #Stability (learning theory) #Stable manifold #Trajectory #msc:32Q05 #msc:34D08 #msc:37D20 #msc:37D45 #msc:70F20 #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1134/s1560354715060027
published in Regular and Chaotic Dynamics 20(6), 649-666 (Pleiades Publishing) · 30 pages, 18 figures
arxiv created 2015/10/13 · openalex publication_date 2015/11/01 · arxiv updated 2016/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Dynamical equations are formulated and a numerical study is provided for selfoscillatory model systems based on the triple linkage hinge mechanism of Thurston–Weeks–Hunt–MacKay. We consider systems with a holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.