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Peer-reviewedCC BY 4.0Physical Review Research

Evaluating criteria for bubbling in coupled chaotic oscillators

  • Giulio Tirabassi1
  • Raul de Palma Aristides2
  • Cristina Masoller3
  • Daniel J. Gauthier4
4 affiliations
  1. 1Universitat de Girona
  2. 2Institute for Cross-Disciplinary Physics and Complex Systems (UIB-CSIC)
  3. 3Departament de Fisica, Universitat Politècnica de Catalunya
  4. 4ResCon Technologies
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Abstract

The stability of the synchronized state of coupled time-varying systems can be predicted with good accuracy for noiseless identical oscillators. Such an assumption, however, is unrealistic for real systems where small heterogeneity and noise are always present. In the case of chaotic oscillators, small heterogeneities and/or noise can generate, due to the existence of unstable sets embedded in the attractor, severe desynchronization bursts, known as , even in the coupling regions that standard linear stability analysis identifies as stable. Here, we analyze the bubbling phenomenon in coupled Rössler and Lorenz chaotic oscillators and predict when bubble-free behavior is expected. We present several different criteria, identifying the one that provides the closest prediction of the minimum coupling strength required for high-quality synchronization during a finite-time simulation.

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Cite

BibTeXRIS
BibTeX
@article{tirabassi2026evaluating,
  title = {{Evaluating criteria for bubbling in coupled chaotic oscillators}},
  author = {Giulio Tirabassi and Raul de Palma Aristides and Cristina Masoller and Daniel J. Gauthier},
  journal = {Physical Review Research},
  year = {2026},
  month = oct,
  doi = {10.1103/ycf8-4sz5},
  url = {http://link.aps.org/doi/10.1103/ycf8-4sz5},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Evaluating criteria for bubbling in coupled chaotic oscillators
AU  - Giulio Tirabassi
AU  - Raul de Palma Aristides
AU  - Cristina Masoller
AU  - Daniel J. Gauthier
PY  - 2026
DA  - 2026/10/29
JO  - Physical Review Research
DO  - 10.1103/ycf8-4sz5
UR  - http://link.aps.org/doi/10.1103/ycf8-4sz5
AB  - The stability of the synchronized state of coupled time-varying systems can be predicted with good accuracy for noiseless identical oscillators. Such an assumption, however, is unrealistic for real systems where small heterogeneity and noise are always present. In the case of chaotic oscillators, small heterogeneities and/or noise can generate, due to the existence of unstable sets embedded in the attractor, severe desynchronization bursts, known as , even in the coupling regions that standard linear stability analysis identifies as stable. Here, we analyze the bubbling phenomenon in coupled Rössler and Lorenz chaotic oscillators and predict when bubble-free behavior is expected. We present several different criteria, identifying the one that provides the closest prediction of the minimum coupling strength required for high-quality synchronization during a finite-time simulation.
SN  - 2643-1564
ER  -