Work

Feedback-delay dependence of the stability of cluster periodic orbits in populations of degrade-and-fire oscillators with common activator

Year: 2025

Type: article

Abstract: Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire oscillators coupled via a common activator protein, full mathematical certifications remained to be provided. Here, we prove from a rigorous mathematical viewpoint that, for the very same model, the synchronized degrade-and-fire oscillations are 1/ unstable with respect to out-of-sync perturbations in absence of delay, and 2/ are otherwise asymptotically stable in presence of delay, no matter how small is its amplitude. To that goal, we proceed to an extensive study of the population dynamics in this system, which in particular identifies the mechanisms of, and related criteria for, the delay-dependent stability of periodic orbits with respect to out-of-sync perturbations. As an additional outcome, the analysis also reveals that, depending on the parameters, multiple stable partially synchronized periodic orbits can coexist with the fully synchronized one.

Source: Journal of Mathematical Biology

DOI: 10.1007/s00285-024-02169-7

Authors: Bastien Fernandez, Matteo Tanzi

Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation, King's College London

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: European Commission, Horizon 2020 Framework Programme