---
_id: '12259'
abstract:
- lang: eng
  text: 'Theoretical foundations of chaos have been predominantly laid out for finite-dimensional
    dynamical systems, such as the three-body problem in classical mechanics and the
    Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena,
    e.g., weather, arise in systems with many (formally infinite) degrees of freedom,
    which limits direct quantitative analysis of such systems using chaos theory.
    In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer
    a bridge between low- and high-dimensional chaotic phenomena by allowing for a
    systematic study of how the former connects to the latter. Specifically, we present
    experimental results, which show the formation of low-dimensional chaotic attractors
    upon destabilization of regular dynamics and a final transition to high-dimensional
    chaos via the merging of distinct chaotic regions through a crisis bifurcation.
    Moreover, we show that the post-crisis dynamics of the system can be rationalized
    as consecutive scatterings from the nonattracting chaotic sets with lifetimes
    following exponential distributions. '
acknowledgement: 'This work was partially funded by the Institute of Science and Technology
  Austria Interdisciplinary Project Committee Grant “Pilot-Wave Hydrodynamics: Chaos
  and Quantum Analogies.”'
article_number: '093138'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: George H
  full_name: Choueiri, George H
  id: 448BD5BC-F248-11E8-B48F-1D18A9856A87
  last_name: Choueiri
- first_name: Balachandra
  full_name: Suri, Balachandra
  id: 47A5E706-F248-11E8-B48F-1D18A9856A87
  last_name: Suri
- first_name: Jack
  full_name: Merrin, Jack
  id: 4515C308-F248-11E8-B48F-1D18A9856A87
  last_name: Merrin
  orcid: 0000-0001-5145-4609
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
- first_name: Nazmi B
  full_name: Budanur, Nazmi B
  id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
  last_name: Budanur
  orcid: 0000-0003-0423-5010
citation:
  ama: 'Choueiri GH, Suri B, Merrin J, Serbyn M, Hof B, Budanur NB. Crises and chaotic
    scattering in hydrodynamic pilot-wave experiments. <i>Chaos: An Interdisciplinary
    Journal of Nonlinear Science</i>. 2022;32(9). doi:<a href="https://doi.org/10.1063/5.0102904">10.1063/5.0102904</a>'
  apa: 'Choueiri, G. H., Suri, B., Merrin, J., Serbyn, M., Hof, B., &#38; Budanur,
    N. B. (2022). Crises and chaotic scattering in hydrodynamic pilot-wave experiments.
    <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. AIP Publishing.
    <a href="https://doi.org/10.1063/5.0102904">https://doi.org/10.1063/5.0102904</a>'
  chicago: 'Choueiri, George H, Balachandra Suri, Jack Merrin, Maksym Serbyn, Björn
    Hof, and Nazmi B Budanur. “Crises and Chaotic Scattering in Hydrodynamic Pilot-Wave
    Experiments.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>.
    AIP Publishing, 2022. <a href="https://doi.org/10.1063/5.0102904">https://doi.org/10.1063/5.0102904</a>.'
  ieee: 'G. H. Choueiri, B. Suri, J. Merrin, M. Serbyn, B. Hof, and N. B. Budanur,
    “Crises and chaotic scattering in hydrodynamic pilot-wave experiments,” <i>Chaos:
    An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32, no. 9. AIP Publishing,
    2022.'
  ista: 'Choueiri GH, Suri B, Merrin J, Serbyn M, Hof B, Budanur NB. 2022. Crises
    and chaotic scattering in hydrodynamic pilot-wave experiments. Chaos: An Interdisciplinary
    Journal of Nonlinear Science. 32(9), 093138.'
  mla: 'Choueiri, George H., et al. “Crises and Chaotic Scattering in Hydrodynamic
    Pilot-Wave Experiments.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>,
    vol. 32, no. 9, 093138, AIP Publishing, 2022, doi:<a href="https://doi.org/10.1063/5.0102904">10.1063/5.0102904</a>.'
  short: 'G.H. Choueiri, B. Suri, J. Merrin, M. Serbyn, B. Hof, N.B. Budanur, Chaos:
    An Interdisciplinary Journal of Nonlinear Science 32 (2022).'
date_created: 2023-01-16T09:58:16Z
date_published: 2022-09-26T00:00:00Z
date_updated: 2023-08-04T09:51:17Z
day: '26'
ddc:
- '530'
department:
- _id: MaSe
- _id: BjHo
- _id: NanoFab
doi: 10.1063/5.0102904
external_id:
  arxiv:
  - '2206.01531'
  isi:
  - '000861009600005'
file:
- access_level: open_access
  checksum: 17881eff8b21969359a2dd64620120ba
  content_type: application/pdf
  creator: dernst
  date_created: 2023-01-30T09:41:12Z
  date_updated: 2023-01-30T09:41:12Z
  file_id: '12445'
  file_name: 2022_Chaos_Choueiri.pdf
  file_size: 3209644
  relation: main_file
  success: 1
file_date_updated: 2023-01-30T09:41:12Z
has_accepted_license: '1'
intvolume: '        32'
isi: 1
issue: '9'
keyword:
- Applied Mathematics
- General Physics and Astronomy
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '09'
oa: 1
oa_version: Published Version
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_identifier:
  eissn:
  - 1089-7682
  issn:
  - 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Crises and chaotic scattering in hydrodynamic pilot-wave experiments
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 32
year: '2022'
...
---
_id: '7563'
abstract:
- lang: eng
  text: "We introduce “state space persistence analysis” for deducing the symbolic
    dynamics of time series data obtained from high-dimensional chaotic attractors.
    To this end, we adapt a topological data analysis technique known as persistent
    homology for the characterization of state space projections of chaotic trajectories
    and periodic orbits. By comparing the shapes along a chaotic trajectory to those
    of the periodic orbits, state space persistence analysis quantifies the shape
    similarity of chaotic trajectory segments and periodic orbits. We demonstrate
    the method by applying it to the three-dimensional Rössler system and a 30-dimensional
    discretization of the Kuramoto–Sivashinsky partial differential equation in (1+1)
    dimensions.\r\nOne way of studying chaotic attractors systematically is through
    their symbolic dynamics, in which one partitions the state space into qualitatively
    different regions and assigns a symbol to each such region.1–3 This yields a “coarse-grained”
    state space of the system, which can then be reduced to a Markov chain encoding
    all possible transitions between the states of the system. While it is possible
    to obtain the symbolic dynamics of low-dimensional chaotic systems with standard
    tools such as Poincaré maps, when applied to high-dimensional systems such as
    turbulent flows, these tools alone are not sufficient to determine symbolic dynamics.4,5
    In this paper, we develop “state space persistence analysis” and demonstrate that
    it can be utilized to infer the symbolic dynamics in very high-dimensional settings."
article_number: '033109'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Gökhan
  full_name: Yalniz, Gökhan
  id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
  last_name: Yalniz
  orcid: 0000-0002-8490-9312
- first_name: Nazmi B
  full_name: Budanur, Nazmi B
  id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
  last_name: Budanur
  orcid: 0000-0003-0423-5010
citation:
  ama: Yalniz G, Budanur NB. Inferring symbolic dynamics of chaotic flows from persistence.
    <i>Chaos</i>. 2020;30(3). doi:<a href="https://doi.org/10.1063/1.5122969">10.1063/1.5122969</a>
  apa: Yalniz, G., &#38; Budanur, N. B. (2020). Inferring symbolic dynamics of chaotic
    flows from persistence. <i>Chaos</i>. AIP Publishing. <a href="https://doi.org/10.1063/1.5122969">https://doi.org/10.1063/1.5122969</a>
  chicago: Yalniz, Gökhan, and Nazmi B Budanur. “Inferring Symbolic Dynamics of Chaotic
    Flows from Persistence.” <i>Chaos</i>. AIP Publishing, 2020. <a href="https://doi.org/10.1063/1.5122969">https://doi.org/10.1063/1.5122969</a>.
  ieee: G. Yalniz and N. B. Budanur, “Inferring symbolic dynamics of chaotic flows
    from persistence,” <i>Chaos</i>, vol. 30, no. 3. AIP Publishing, 2020.
  ista: Yalniz G, Budanur NB. 2020. Inferring symbolic dynamics of chaotic flows from
    persistence. Chaos. 30(3), 033109.
  mla: Yalniz, Gökhan, and Nazmi B. Budanur. “Inferring Symbolic Dynamics of Chaotic
    Flows from Persistence.” <i>Chaos</i>, vol. 30, no. 3, 033109, AIP Publishing,
    2020, doi:<a href="https://doi.org/10.1063/1.5122969">10.1063/1.5122969</a>.
  short: G. Yalniz, N.B. Budanur, Chaos 30 (2020).
date_created: 2020-03-04T08:06:25Z
date_published: 2020-03-03T00:00:00Z
date_updated: 2023-08-18T06:47:16Z
day: '03'
department:
- _id: BjHo
doi: 10.1063/1.5122969
external_id:
  arxiv:
  - '1910.04584'
  isi:
  - '000519254800002'
intvolume: '        30'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1063/1.5122969
month: '03'
oa: 1
oa_version: Published Version
publication: Chaos
publication_identifier:
  eissn:
  - 1089-7682
  issn:
  - 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Inferring symbolic dynamics of chaotic flows from persistence
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 30
year: '2020'
...
---
_id: '5878'
abstract:
- lang: eng
  text: We consider the motion of a droplet bouncing on a vibrating bath of the same
    fluid in the presence of a central potential. We formulate a rotation symmetry-reduced
    description of this system, which allows for the straightforward application of
    dynamical systems theory tools. As an illustration of the utility of the symmetry
    reduction, we apply it to a model of the pilot-wave system with a central harmonic
    force. We begin our analysis by identifying local bifurcations and the onset of
    chaos. We then describe the emergence of chaotic regions and their merging bifurcations,
    which lead to the formation of a global attractor. In this final regime, the droplet’s
    angular momentum spontaneously changes its sign as observed in the experiments
    of Perrard et al.
article_number: '013122'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nazmi B
  full_name: Budanur, Nazmi B
  id: 3EA1010E-F248-11E8-B48F-1D18A9856A87
  last_name: Budanur
  orcid: 0000-0003-0423-5010
- first_name: Marc
  full_name: Fleury, Marc
  last_name: Fleury
citation:
  ama: 'Budanur NB, Fleury M. State space geometry of the chaotic pilot-wave hydrodynamics.
    <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 2019;29(1). doi:<a
    href="https://doi.org/10.1063/1.5058279">10.1063/1.5058279</a>'
  apa: 'Budanur, N. B., &#38; Fleury, M. (2019). State space geometry of the chaotic
    pilot-wave hydrodynamics. <i>Chaos: An Interdisciplinary Journal of Nonlinear
    Science</i>. AIP Publishing. <a href="https://doi.org/10.1063/1.5058279">https://doi.org/10.1063/1.5058279</a>'
  chicago: 'Budanur, Nazmi B, and Marc Fleury. “State Space Geometry of the Chaotic
    Pilot-Wave Hydrodynamics.” <i>Chaos: An Interdisciplinary Journal of Nonlinear
    Science</i>. AIP Publishing, 2019. <a href="https://doi.org/10.1063/1.5058279">https://doi.org/10.1063/1.5058279</a>.'
  ieee: 'N. B. Budanur and M. Fleury, “State space geometry of the chaotic pilot-wave
    hydrodynamics,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>,
    vol. 29, no. 1. AIP Publishing, 2019.'
  ista: 'Budanur NB, Fleury M. 2019. State space geometry of the chaotic pilot-wave
    hydrodynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science. 29(1),
    013122.'
  mla: 'Budanur, Nazmi B., and Marc Fleury. “State Space Geometry of the Chaotic Pilot-Wave
    Hydrodynamics.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>,
    vol. 29, no. 1, 013122, AIP Publishing, 2019, doi:<a href="https://doi.org/10.1063/1.5058279">10.1063/1.5058279</a>.'
  short: 'N.B. Budanur, M. Fleury, Chaos: An Interdisciplinary Journal of Nonlinear
    Science 29 (2019).'
date_created: 2019-01-23T08:35:09Z
date_published: 2019-01-22T00:00:00Z
date_updated: 2023-08-25T10:16:11Z
day: '22'
department:
- _id: BjHo
doi: 10.1063/1.5058279
external_id:
  arxiv:
  - '1812.09011'
  isi:
  - '000457409100028'
intvolume: '        29'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1812.09011
month: '01'
oa: 1
oa_version: Preprint
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_identifier:
  eissn:
  - 1089-7682
  issn:
  - 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
related_material:
  link:
  - relation: erratum
    url: https://aip.scitation.org/doi/abs/10.1063/1.5097157
scopus_import: '1'
status: public
title: State space geometry of the chaotic pilot-wave hydrodynamics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 29
year: '2019'
...