Bifurcation of 3-Torus Attractor in Certain Continuous-Time Dynamical Systems*. Issue 18 (2015)

• Record Type: Journal Article
• Authors: Kamiyama, Kyohei; Endo, Tetsuro; Komuro, Motomasa
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 18(2015)
• Page Start: 122
• Page End: 126
• Publication Date: 2015
• Subjects: Quasi-periodic solution -- Torus -- Lyapunov exponent -- Lyapunov bundle -- Saddle-node bifurcation -- Neimark-Sacker bifurcation; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.11.022
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: Previously, we investigated the bifurcation of 2-torus attractor in continuous-time dynamical systems. The systems we investigated was a phase-locked loop with two inputs and a three-coupled van der Pol oscillators. The former example demonstrated saddle-node and double covering bifurcations and the latter a Neimark-Sacker bifurcation of 2-torus. Lyapunov exponents and Lyapunov bundles were used to analyse these bifurcations. In this paper, we investigate bifurcation of 3-torus in the phase-locked loop with three sinusoidal inputs and the four-coupled van der Pol oscillators. Our method to analyse bifurcation of 3-torus uses Poincare map and Poincare slice together with Lyapunov exponents and Lyapunov bundles.