Synchronisation is a well-known phenomenon that plays a key role in physics, biology, and neuroscience, to cite a few. Typical examples are when people clap in unison at the end of a concert, or when heart cells synchronise to make the heart beat. My research on synchronisation focuses on the effects of two ingredients: (1) higher-order interactions, that is when oscillators interact in groups, and (2) time-varying parameters,
Synchronisation with higher-order interactions
Evidence suggests, though, that higher-order interactions are important to fully capture complex processes. To study this, we consider generalisations of the Kuramoto model, where we include interactions terms between two or more oscilators. See my othr work on higher-order networks here.
References
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Collective dynamics on higher-order networks, 2025 — F. Battiston, C. Bick, M. Lucas, A. P. Millán, P. S. Skardal, and Y. Zhang
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Hamiltonian control to desynchronize Kuramoto oscillators with higher-order interactions, Physical Review E, 2025 — M. Moriamé, M. Lucas, and T. Carletti
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Deeper but smaller: Higher-order interactions increase linear stability but shrink basins, Science Advances, 2024 — Y. Zhang, P. S. Skardal, F. Battiston, G. Petri, and M. Lucas
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A unified framework for Simplicial Kuramoto models, Chaos, 2024 — M. Nurisso, A. Arnaudon, M. Lucas, R. L. Peach, P. Expert, F. Vaccarino, and G. Petri
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Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes, Nature Communications, 2023 — Y. Zhang*, M. Lucas*, and F. Battiston
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Multiorder Laplacian for Kuramoto Dynamics with Higher-Order Interactions, In Higher-Order Systems, 2022 — M. Lucas, G. Cencetti, and F. Battiston
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Multiorder Laplacian for synchronization in higher-order networks, Physical Review Research, 2020 — M. Lucas, G. Cencetti, and F. Battiston
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Networks beyond pairwise interactions: structure and dynamics, Physics Reports, 2020 — F. Battiston, G. Cencetti, I. Iacopini, V. Latora, M. Lucas, A. Patania, J.-G. Young, and G. Petri
Synchronisation with time-varying parameters
A lot of theoretical work exists on synchronisation, but mostly considers the frequencies and interaction network to be constant. In nature, and in living systems in particular, however, frequencies change all the time. Imagine how our heartbeat changes when we are calm, stressed, or scared. This is what motivates our studies on synchronisation between oscillators with time-varying parameters. In particular, in different studies, we consider time-varying frequencies, coupling strengths, and network structure.
References
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Stabilization of cyclic processes by slowly varying forcing, Chaos, 2021 — J. Newman, M. Lucas, and A. Stefanovska
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Synchronisation and Non-autonomicity, In Physics of Biological Oscillators, 2021 — M. Lucas, J. Newman, and A. Stefanovska
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Non-asymptotic-time Dynamics, In Physics of Biological Oscillators, 2021 — J. Newman, M. Lucas, and A. Stefanovska
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Synchronisation and stability in nonautonomous oscillatory systems, Lancaster University and University of Florence, 2019 — M. Lucas
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Nonautonomous driving induces stability in network of identical oscillators, Physical Review E, 2019 — M. Lucas, D. Fanelli, and A. Stefanovska
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Desynchronization induced by time-varying network, Europhys. Lett., 2018 — M. Lucas, D. Fanelli, T. Carletti, and J. Petit
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Stabilization of dynamics of oscillatory systems by nonautonomous perturbation, Physical Review E, 2018 — M. Lucas, J. Newman, and A. Stefanovska