Three-Dimensional Torus Breakdown and Chaos With Two Zero Lyapunov Exponents in Coupled Radio-Physical Generators
Nataliya Stankevich, Natalya A. Shchegoleva, I. R. Sataev, А. П. Кузнецов
Abstract
Abstract Using an example a system of two coupled generators of quasi-periodic oscillations, we study the occurrence of chaotic dynamics with one positive, two zero, and several negative Lyapunov exponents. It is shown that such dynamic arises as a result of a sequence of bifurcations of two-frequency torus doubling and involves saddle tori occurring at their doublings. This transition is associated with typical structure of parameter plane, like cross-road area and shrimp-shaped structures, based on the two-frequency quasi-periodic dynamics. Using double Poincaré section, we have shown destruction of three-frequency torus.
Topics & Concepts
Lyapunov exponentTorusChaoticSaddlePhysicsZero (linguistics)MathematicsPlane (geometry)Mathematical analysisStatistical physicsNonlinear systemGeometryQuantum mechanicsComputer scienceMathematical optimizationArtificial intelligenceLinguisticsPhilosophyQuantum chaos and dynamical systemsNonlinear Dynamics and Pattern FormationChaos control and synchronization