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PreprintCC BY 4.0arXiv

Spontaneous Spirals in Spatial Systems

  • Wim Hordijk
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Abstract

Several chemical and biological systems produce spontaneous spirals in their dynamical behavior, such as the Belousov-Zhabotinsky reaction in chemistry and the slime mold Dictyostelium in biology. In a previous study, such spiral wave formation was accurately replicated with a computational spatial system known as the Ideal Storage Cellular Automaton Model (ISCAM). Here, a more detailed investigation is presented of the ability of this model to generate spontaneous spirals depending on its parameter values. A dynamical systems analysis is performed, and bifurcation diagrams, phase space diagrams, and snapshots of the model's spatial dynamics are presented for a range of parameter values. This analysis reveals that spiral waves can only be sustained in the system when the parameter values of the model fall well within the regime of a so-called Neimark-Sacker bifurcation.

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Cite

BibTeXRIS
BibTeX
@misc{hordijk2026spontaneous,
  title = {{Spontaneous Spirals in Spatial Systems}},
  author = {Wim Hordijk},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38710},
  eprint = {2610.38710},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38710},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spontaneous Spirals in Spatial Systems
AU  - Wim Hordijk
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38710
UR  - https://arxiv.org/abs/2610.38710
AB  - Several chemical and biological systems produce spontaneous spirals in their dynamical behavior, such as the Belousov-Zhabotinsky reaction in chemistry and the slime mold Dictyostelium in biology. In a previous study, such spiral wave formation was accurately replicated with a computational spatial system known as the Ideal Storage Cellular Automaton Model (ISCAM). Here, a more detailed investigation is presented of the ability of this model to generate spontaneous spirals depending on its parameter values. A dynamical systems analysis is performed, and bifurcation diagrams, phase space diagrams, and snapshots of the model's spatial dynamics are presented for a range of parameter values. This analysis reveals that spiral waves can only be sustained in the system when the parameter values of the model fall well within the regime of a so-called Neimark-Sacker bifurcation.
ER  -