Route to hyperchaos in a system of coupled oscillators with multistability

NJ McCullen, P. Moresco

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This work presents the results of a detailed experimental study into the transition between synchronized, low-dimensional, and unsynchronized, high-dimensional dynamics using a system of coupled electronic chaotic oscillators. Novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets. These originate from initially multistable low-dimensional attractors which experience a smooth transition from low- to high-dimensional chaotic behavior, losing stability through a bubbling bifurcation. Numerical techniques were also employed to verify and expand on the experimental results, giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor. This particular route to hyperchaos also results in the possibility of phenomena (such as unstable dimension variability) that can be a major obstruction to shadowing and predictability in chaotic systems.
Original languageEnglish
Article number046212
Number of pages9
JournalPhysical Review E (PRE)
Volume83
Issue number4
DOIs
Publication statusPublished - 2011

Fingerprint

routes
oscillators
electronics

Cite this

Route to hyperchaos in a system of coupled oscillators with multistability. / McCullen, NJ; Moresco, P.

In: Physical Review E (PRE), Vol. 83, No. 4, 046212, 2011.

Research output: Contribution to journalArticle

@article{de792fc7291c4722b9b6fc70252a202d,
title = "Route to hyperchaos in a system of coupled oscillators with multistability",
abstract = "This work presents the results of a detailed experimental study into the transition between synchronized, low-dimensional, and unsynchronized, high-dimensional dynamics using a system of coupled electronic chaotic oscillators. Novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets. These originate from initially multistable low-dimensional attractors which experience a smooth transition from low- to high-dimensional chaotic behavior, losing stability through a bubbling bifurcation. Numerical techniques were also employed to verify and expand on the experimental results, giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor. This particular route to hyperchaos also results in the possibility of phenomena (such as unstable dimension variability) that can be a major obstruction to shadowing and predictability in chaotic systems.",
author = "NJ McCullen and P. Moresco",
year = "2011",
doi = "10.1103/PhysRevE.83.046212",
language = "English",
volume = "83",
journal = "Physical Review E (PRE)",
number = "4",

}

TY - JOUR

T1 - Route to hyperchaos in a system of coupled oscillators with multistability

AU - McCullen, NJ

AU - Moresco, P.

PY - 2011

Y1 - 2011

N2 - This work presents the results of a detailed experimental study into the transition between synchronized, low-dimensional, and unsynchronized, high-dimensional dynamics using a system of coupled electronic chaotic oscillators. Novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets. These originate from initially multistable low-dimensional attractors which experience a smooth transition from low- to high-dimensional chaotic behavior, losing stability through a bubbling bifurcation. Numerical techniques were also employed to verify and expand on the experimental results, giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor. This particular route to hyperchaos also results in the possibility of phenomena (such as unstable dimension variability) that can be a major obstruction to shadowing and predictability in chaotic systems.

AB - This work presents the results of a detailed experimental study into the transition between synchronized, low-dimensional, and unsynchronized, high-dimensional dynamics using a system of coupled electronic chaotic oscillators. Novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets. These originate from initially multistable low-dimensional attractors which experience a smooth transition from low- to high-dimensional chaotic behavior, losing stability through a bubbling bifurcation. Numerical techniques were also employed to verify and expand on the experimental results, giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor. This particular route to hyperchaos also results in the possibility of phenomena (such as unstable dimension variability) that can be a major obstruction to shadowing and predictability in chaotic systems.

UR - http://www.scopus.com/inward/record.url?scp=79961074744&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1103/PhysRevE.83.046212

U2 - 10.1103/PhysRevE.83.046212

DO - 10.1103/PhysRevE.83.046212

M3 - Article

VL - 83

JO - Physical Review E (PRE)

JF - Physical Review E (PRE)

IS - 4

M1 - 046212

ER -