ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR

DOI10.1142/S0218127408020835zbMath1147.34323OpenAlexW2087417978MaRDI QIDQ3536125

Kazuyuki Aihara, Naohiko Inaba, Takashi Tsubouchi, Munehisa Sekikawa

Publication date: 17 November 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127408020835

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Low-dimensional dynamical systems (37E99) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (7)

Three-dimensional tori and Arnold tongues ⋮ Novel bifurcation structure generated in piecewise-linear three-LC resonant circuit and its Lyapunov analysis ⋮ Nested mixed-mode oscillations ⋮ Duffing-van der Pol oscillator type dynamics in Murali-Lakshmanan-Chua (MLC) circuit ⋮ Chaos via torus breakdown from a four-dimensional autonomous oscillator with two diodes ⋮ Classification of parametrically constrained bifurcations ⋮ Novel routes to chaos through torus breakdown in non-invertible maps

Cites Work

• Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
• Sigma-finite invariant measures for smooth mappings of the circle
• Devil's staircase route to chaos in a forced relaxation oscillator
• Chaos via duck solution breakdown in a piecewise linear van der Pol oscillator driven by an extremely small periodic perturbation
• Supercritical Behavior of Disordered Orbits of a Circle Map
• Entropy, Lyapunov exponents, and Hausdorff dimension in differentiable dynamical systems
• Bifurcation of periodic responses in forced dynamic nonlinear circuits: Computation of bifurcation values of the system parameters
• Period Three Implies Chaos
• FRACTIONAL HARMONIC SYNCHRONIZATION IN THE DUFFING-RAYLEIGH DIFFERENTIAL EQUATION
• ON A "CROSSROAD AREA–SPRING AREA" TRANSITION OCCURRING IN A DUFFING–RAYLEIGH EQUATION WITH A PERIODICAL EXCITATION
• REDUCIBLE FRACTIONAL HARMONICS GENERATED BY THE NONAUTONOMOUS DUFFING–RAYLEIGH EQUATION: POCKETS OF REDUCIBLE HARMONICS AND ARNOLD'S TONGUES

This page was built for publication: ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR