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MULTIPLE LOCAL AND GLOBAL BIFURCATIONS AND THEIR ROLE IN QUORUM SENSING DYNAMICS

Part of: Local and nonlocal bifurcation theory Smooth dynamical systems: general theory Mathematical biology in general Qualitative theory Special Collection in honour of Professor Bernd Krauskopf

Published online by Cambridge University Press:  09 April 2025

M. HARRIS Open the ORCID record for M. HARRIS [Opens in a new window] ,
V. RIVERA–ESTAY Open the ORCID record for V. RIVERA–ESTAY [Opens in a new window] ,
P. AGUIRRE Open the ORCID record for P. AGUIRRE [Opens in a new window]  and
V. F. BREÑA–MEDINA Open the ORCID record for V. F. BREÑA–MEDINA [Opens in a new window]
M. HARRIS
Affiliation:
Department of Computational Medicine, UCLA, Los Angeles, CA 90095, USA; e-mail: mharris94@g.ucla.edu
V. RIVERA–ESTAY
Affiliation:
Departamento de Matemática, Física y Estadística, Universidad Católica del Maule, San Miguel 3605, Talca, Chile; e-mail: vivianarivera.mate@gmail.com
P. AGUIRRE
Affiliation:
Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile; e-mail: pablo.aguirre@usm.cl
V. F. BREÑA–MEDINA*
Affiliation:
Departmento de Matemáticas, ITAM, Río Hondo 1, Ciudad de México 01080, Mexico
*
e-mail: victor.brena@itam.mx
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Abstract

Quorum sensing governs bacterial communication, playing a crucial role in regulating population behaviour. We propose a mathematical model that uncovers chaotic dynamics within quorum sensing networks, highlighting challenges to predictability. The model explores interactions between autoinducers and two bacterial subtypes, revealing oscillatory dynamics in both a constant autoinducer submodel and the full three-component model. In the latter case, we find that the complicated dynamics can be explained by the presence of homoclinic Shilnikov bifurcations. We employ a combination of normal-form analysis and numerical continuation methods to analyse the system.

Keywords

homoclinic bifurcationnormal formschaotic dynamicsquorum sensing

MSC classification

Primary: 34C23: Bifurcation
Secondary: 37G05: Normal forms 37G15: Bifurcations of limit cycles and periodic orbits 37C29: Homoclinic and heteroclinic orbits 37G20: Hyperbolic singular points with homoclinic trajectories 92B25: Biological rhythms and synchronization

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 67 , 2025 , e17
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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