https://doi.org/10.1140/epje/s10189-026-00559-x
Research – Flowing Matter
Coupled interplays between proliferation and hydrodynamic interactions modulate the transport of chemotactic entities
1
Centre for Research in Infectious Disease, P.O. Box 13591, Yaounde, Cameroon
2
African Centre for Advanced Studies, P.O. Box 4477, Yaounde, Cameroon
3
Department of Mathematics and Physical Sciences, National Advanced School of Engineering of Yaounde, University of Yaounde I, P.O. Box 8390, Yaounde, Cameroon
a
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Received:
29
September
2025
Accepted:
19
January
2026
Published online:
24
February
2026
Abstract
This study investigates the stability properties of two interacting chemotactic populations by introducing an extended mathematical model that simultaneously incorporates competitive hydrodynamic interactions and kinetic growth dynamics. Using a standard plane wave analysis, we demonstrate that the interplay between hydrodynamic and kinetic interactions governs the system’s stability. Specifically, the system remains stable for long wave vectors when strong-strong kinetic interactions are coupled with either weak-weak or strong-weak hydrodynamic interactions. Conversely, stability for short wave vectors is achieved when weak-weak kinetic interactions are paired with similar hydrodynamic configurations. To explore localized dynamics, we perform a generalized linear stability analysis using spatially localized functions. This reveals the emergence of rapid oscillations that modulate both stationary and non-stationary wave patterns. Modulated structures are sensitive to the choice of the envelope function: waves initiated with Gaussian-type profiles are more prone to instability than those generated with secant-type functions. Numerical simulations further illustrate the formation of stable non-uniformly distributed structures. The generalized perturbation framework presented here highlights the delicate balance between hydrodynamics and competitive interactions occurring within biological tissues during invasion, showcasing new insights into collective transport, pattern formation, and strategies for organ repair.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epje/s10189-026-00559-x.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
