Chaos via torus breakdown from a four-dimensional autonomous oscillator with two diodes
type: Item
instance of: scholarly article
title: Chaos via torus breakdown from a four-dimensional autonomous oscillator with two diodes
zbMATH Open document ID: 1228.94034
author: Naohiko Inaba
author: Yoshifumi Nishio
author: Tetsuro Endo
published in: Physica D
publication date: 2011-06-14T00:00:00Z
review text: The authors study a four-dimensional autonomous circuit with two diodes, which is a simple autonomous oscillator as a fourth-order circuit. The circuit is examined experimentally and numerically. Moreover, in the case where the diodes are assumed to operate as switches, the Poincaré mapping is derived as a circle map. Torus breakdown into chaos is observed experimentally and numerically, and it is explained via the Poincaré mapping.
Mathematics Subject Classification ID: 94C05
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5907633
zbMATH Keywords: chaos
zbMATH Keywords: torus breakdown
zbMATH Keywords: nonlinear circuit
reviewed by: David E. Hurtubise
MaRDI profile type: Publication
full work available at URL: j.physd.2011.01.005
OpenAlex ID: W2021755322
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Q3736576
cites work: Q3127082
cites work: Bifurcation of periodic responses in forced dynamic nonlinear circuits: Computation of bifurcation values of the system parameters
cites work: Bifurcations in a mathematical model for circadian oscillations of clock genes
cites work: The double scroll
cites work: Birth and death of the double scroll
cites work: Reality of chaos in four-dimensional hysteretic circuits
cites work: The double scroll family
cites work: A second order differential equation with singular solutions
cites work: Qualitative analysis of the periodically forced relaxation oscillations
cites work: Q3878949
cites work: Local and global behavior near homoclinic orbits
cites work: Quasiperiodicity and torus breakdown in a power electronic dc/dc converter
cites work: Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems
cites work: Routes to chaos in high-dimensional dynamical systems: a qualitative numerical study
cites work: Bifurcations and chaos in a system with impacts
cites work: Tori and Klein bottles in four-dimensional chaotic flows
cites work: On fundamental bifurcations from a hysteresis hyperchaos generator
cites work: Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
cites work: Chaos via duck solution breakdown in a piecewise linear van der Pol oscillator driven by an extremely small periodic perturbation
cites work: ANALYSIS OF TORUS BREAKDOWN INTO CHAOS IN A CONSTRAINT DUFFING VAN DER POL OSCILLATOR
cites work: Sigma-finite invariant measures for smooth mappings of the circle
cites work: Universal properties of the transition from quasi-periodicity to chaos in dissipative systems
cites work: Supercritical behavior of disordered orbits of a circle map.
DOI: 10.1016/J.PHYSD.2011.01.005
description: scientific article; zbMATH DE number 5907633