Traveling waves, phase separation and pattern formation in the active stepping stone model
Abstract
Selective advantage leads to the proliferation of a species into an ecosystem. On the other hand, self-propulsion can lead to dynamic clustering of individuals. To analyze the intricate effects produced by such competing processes, we introduce a minimal model for a proliferating active population, where run-and-tumble migration is combined with a stochastic birth-death process. Beginning with the microscopic dynamics of the particles, we derive the corresponding hydrodynamic equations and validate them through numerical simulations. We demonstrate that the inclusion of activity leads to the emergence of novel morphological patterns, which are sensitive to the specific rules governing migration. Furthermore, we show that activity significantly alters the characteristics of invasion waves, increasing their propagation speed. However, beyond a threshold, excessive activity disrupts the wave-like nature of the invasion process. We also extend our study to two dimensions and analyze the instabilities that lead to pattern formation in such systems.
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BibTeX
@misc{bhutia2026traveling,
title = {{Traveling waves, phase separation and pattern formation in the active stepping stone model}},
author = {Rashmiranjan Bhutia and Prasad Perlekar and Kabir Ramola},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02346},
eprint = {2610.02346},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02346},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Traveling waves, phase separation and pattern formation in the active stepping stone model
AU - Rashmiranjan Bhutia
AU - Prasad Perlekar
AU - Kabir Ramola
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02346
UR - https://arxiv.org/abs/2610.02346
AB - Selective advantage leads to the proliferation of a species into an ecosystem. On the other hand, self-propulsion can lead to dynamic clustering of individuals. To analyze the intricate effects produced by such competing processes, we introduce a minimal model for a proliferating active population, where run-and-tumble migration is combined with a stochastic birth-death process. Beginning with the microscopic dynamics of the particles, we derive the corresponding hydrodynamic equations and validate them through numerical simulations. We demonstrate that the inclusion of activity leads to the emergence of novel morphological patterns, which are sensitive to the specific rules governing migration. Furthermore, we show that activity significantly alters the characteristics of invasion waves, increasing their propagation speed. However, beyond a threshold, excessive activity disrupts the wave-like nature of the invasion process. We also extend our study to two dimensions and analyze the instabilities that lead to pattern formation in such systems.
ER -