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PreprintCC BY-NC 4.0HAL

When Self-Generated Gradients meet Cell Division: Waves and Speed Selection in a Minimal Model

  • Mete Demircigil
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Abstract

We study a minimal Go-or-Grow model for cell propagation driven by self-generated nutrient gradients, coupling diffusion, division, and directed migration through a discontinuous switching mechanism. We establish local well-posedness, characterize all positive bounded traveling waves, and derive an explicit minimal wave speed. Using neutral fractions, we show that minimal waves undergo a pulled-to-pushed transition as the migratory bias increases, while nonminimal waves remain pulled. Finally, we obtain a weak speed-selection result that singles out the minimal wave speed as the only possible limiting propagation speed.

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Cite

BibTeXRIS
BibTeX
@misc{demircigil2026when,
  title = {{When Self-Generated Gradients meet Cell Division: Waves and Speed Selection in a Minimal Model}},
  author = {Mete Demircigil},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  eprint = {2203.05204},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-03601815v2},
  note = {CC BY-NC 4.0},
}
RIS
TY  - UNPB
TI  - When Self-Generated Gradients meet Cell Division: Waves and Speed Selection in a Minimal Model
AU  - Mete Demircigil
PY  - 2026
DA  - 2026/10/06
PB  - HAL
UR  - https://hal.science/hal-03601815v2
AB  - We study a minimal Go-or-Grow model for cell propagation driven by self-generated nutrient gradients, coupling diffusion, division, and directed migration through a discontinuous switching mechanism. We establish local well-posedness, characterize all positive bounded traveling waves, and derive an explicit minimal wave speed. Using neutral fractions, we show that minimal waves undergo a pulled-to-pushed transition as the migratory bias increases, while nonminimal waves remain pulled. Finally, we obtain a weak speed-selection result that singles out the minimal wave speed as the only possible limiting propagation speed.
ER  -