Numerical test for hyperbolicity in chaotic systems with multiple time delays

2017/08/15 by Pavel V. Kuptsov, С. П. Кузнецов, Sergey P. Kuznetsov · 11 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Chaos control and synchronization #Chaotic #Chaotic systems #Computer science #Control (management) #Control theory (sociology) #Covariant transformation #Extension (predicate logic) #Geometry #Lyapunov exponent #Mathematical Dynamics and Fractals #Mathematics #Phase space #Physics #Quantum chaos and dynamical systems #nlin.CD

paper · pdf · doi:10.1016/j.cnsns.2017.08.016

published in Communications in Nonlinear Science and Numerical Simulation 56, 227-239 (Elsevier BV) · 16 pages, 3 figures

arxiv created 2017/08/15 · openalex publication_date 2017/08/17 · openalex created_date 2017/08/31 · arxiv updated 2017/09/13 · openalex updated_date 2026/08/05

Abstract

We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is based on the theory of covariant Lyapunov vectors and provides an efficient algorithm applicable for systems with high-dimensional phase space. Three particular examples of time-delay systems are analyzed and in all cases the expected hyperbolicity is confirmed.

Citations

• Attractor of Smale - Williams type in an autonomous time-delay system
• The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos
• Matplotlib: A 2D Graphics Environment
• A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems
• Characterizing Dynamics with Covariant Lyapunov Vectors
• Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories
• Differentiable dynamical systems