Study of the Observability and Controllability of Synchronization Models for Healthcare Applications

Synchronization and desynchronization play a key role in various biological and medical fields, ranging from neuroscience to cardiology, as well as in glucose regulation and tumor growth. These phenomena open new biomedical perspectives, such as identifying biomarkers based on the synchronization state of cellular subpopulations or the controlled induction of specific dynamics for targeted therapeutic applications. Phase-coupled oscillator networks, such as the Kuramoto model [1], are widely used to understand the underlying mechanisms of these complex dynamics. They provide a robust theoretical framework for analyzing nonlinear interactions and network structures in real biological systems, enabling practical applications in neurology, oncology, and other disciplines [2].

Among these models, Kuramoto equations stand out by modeling nodes with intrinsic frequencies and nonlinear couplings. Although initially developed for infinite networks, recent advancements have focused on finite networks and "small-world" architectures. These studies have explored how network density and structure influence synchronization and global dynamics, offering predictions applicable to real experimental contexts [3]. Thus, oscillator models provide valuable tools for understanding and controlling complex biological processes [4] while bridging theoretical approaches with experimental reality.

The aim of this thesis is to study phase-coupled oscillator models through the lens of observability and controllability, to explore the conditions necessary for developing new biomarkers and therapeutic strategies for network structures corresponding to biological systems. The proposed approach is twofold:

1. To develop a theoretical and computational method that incorporates the structure and nature of the network—considering its architecture, node properties, and couplings—integrating observability and controllability concerns from the earliest stages of defining the biological network.

2. To demonstrate the feasibility of this approach by reusing diverse application contexts and experimental means tied to ongoing and funded projects within the laboratory.

Expected outcome: The current PhD project aims at pushing the boundaries in designing novel electroceuticals in various and challenging contexts. We expect:

● Novel methods and computational tools for a modeling framework used in numerous scientific fields,

● Development of proof-of-concept experiments in neuroscience and cancer therapies, work with expert scientist in diverse projects

● Publications in high-impact scientific journals and conferences.

Scientific references:

[1] Acebrón, J. A., Bonilla, L. L., Pérez Vicente, C. J., Ritort, F., & Spigler, R. (2005). The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of modern physics, 77(1), 137-185. [2] Lodi, M., Panahi, S., Sorrentino, F., Torcini, A., & Storace, M. (2024). Patterns of synchronized clusters in adaptive networks. Communications Physics, 7(1), 198. [3] Budzinski, R. C., Nguyen, T. T., Benigno, G. B., Đoàn, J., Mináč, J., Sejnowski, T. J., & Muller, L. E. (2023). Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays. Physical Review Research, 5(1), 013159. [4] Lynn, C. W., & Bassett, D. S. (2019). The physics of brain network structure, function and control. Nature Reviews Physics, 1(5), 318-332.

Le laboratoire de l’Intégration du Matériau au Système a été créé le 1er janvier 2007, par la fusion de trois unités de recherche bordelaises, avec une stratégie scientifique commune de développement principalement centrée dans le domaine des Sciences et de l’Ingénierie des Systèmes, à la convergence des Sciences et Technologies de l’Information et de la Communication , et des Sciences pour l’Ingénieur .

Le laboratoire est rattaché à trois tutelles, le CNRS, l’Université de Bordeaux et Bordeaux Aquitaine INP.

Au CNRS, l’UMR5218 est rattachée en principal à l’Institut des Sciences de l’Ingénierie et des Systèmes et en secondaire à l’Institut des Sciences de l’Information et de leurs Interactions .

This PhD subject is highly transdisciplinary. We will consider applications from various backgrounds, from applied mathematics to engineering (control theory or electrical engineering). The candidate should have:

● Knowledge in system modeling (nonlinear systems, nonlinear ODE, computational simulation and numerical methods),

● Knowledge of programming in python/matlab, basic knowledge of C,

● Strong interest in biology and biomedical applications,

● Strong interest in team work and interaction, fluent communication in english.