Seminar Details
2024-09-17 (14h) : Emergence and control of synchronization patterns in systems with higher-order interactions
At Maxwell building (Shannon room)
Organized by Mathematical Engineering
Speaker :
Riccardo Muolo (Tokyo Institute of Technology)
Abstract :
Synchronization is a ubiquitous emergent phenomenon in which an ensemble of elementary units behaves in unison due to their interactions [1]. Given the pervasiveness of synchronization, understanding how it is achieved is a fundamental question. In particular, the nature of the interactions among oscillators has strong consequences on the transition to synchronization. To tackle this issue, it is convenient to consider phase models in which each oscillator is described solely in terms of a phase variable. According to phase reduction theory, the phase model captures the dynamics completely when the coupling among the oscillators is sufficiently weak [2]. If one considers only pairwise interactions, the synchronization transition is described by a Kuramoto-type model. Despite the versatility of such an approach, the classical theory of synchronization is solely based on pairwise interactions, while, in many systems, the interactions are intrinsically higher-order (many-body) rather than pairwise [3]. In fact, many examples show that a pairwise description is not sufficient to match the theory with observations and, additionally, higher-order interactions appear naturally when phase reduction is performed up to higher orders [4]. It was also shown that extensions of the Kuramoto model including higher-order interactions exhibit an explosive transition to synchrony and other rich behaviors [5].
I will start by introducing the phase reduction theory and highlight the universality of phase models. Then, after discussing the basics of higher-order interactions, I will present a recent work where we analyzed the collective dynamics of the simplest minimal extension of the Kuramoto-type phase model for identical globally coupled oscillators subject to two- and three-body interactions and showed how the many-body interactions greatly enrich the synchronization patterns of the system [6]. In the last part of the seminar, I will briefly introduce an intriguing synchronization pattern in which coherent and incoherent oscillators coexist, called chimera states [7]. Such patterns are known to be elusive and characterized by a very short life-time when the interactions are pairwise, but are enhanced by the presence higher-order interactions [9]. This fact can be exploited by using a pinning control approach: in fact, controlling the emergence of chimera states in systems with higher-order interactions is much easier and efficient if compared with the classic network framework [10].
This is joint work with Hiroya Nakao (Tokyo Institute of Technology, Japan), Shigefumi Hata (Kagoshima University, Japan), Iván León (University of Cantabria, Spain), Lucia Valentina Gambuzza and Mattia Frasca (University of Catania, Italy)
References:
[1] Kuramoto Y., Chemical Oscillations, Waves, and Turbulence. Springer-Verlag, 1984.
[2] Nakao H., Phase reduction approach to synchronisation of nonlinear oscillators. Cont. Phys., 57(2): 188-214, 2016.
[3] Battiston F. et al., Networks beyond pairwise interactions: Structure and dynamics. Phys. Rep., 84: 1-92, 2020.
[4] León I. and Pazó D., Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation. Phys. Rev. E, 100(1): 012211, 2019.
[5] Skardal P.S. and Arenas A., Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes. Phys. Rev. Lett., 122(84): 248301, 2019.
[6] León I., Muolo R., Hata S. and Nakao H., Higher-order interactions induce anomalous transitions to synchrony. Chaos 34, 013105, 2024.
[7] Zakharova A., Chimera Patterns in Networks. Interplay between Dynamics, Structure, Noise, and Delay. Springer, 2020.
[8] Kuramoto Y. and Battogtokh D, Coexistence of coherence and incoherence in nonlocally coupled phase oscillators. Nonlinear Phenom. Complex Syst. 5, 2002.
[9] Muolo R., Njougouo T., Gambuzza L.V., Carletti T. and Frasca M., Phase chimera states on nonlocal hyperrings. Phys. Rev. E 109, L022201, 2024.
[10] Muolo R., Gambuzza L.V., Nakao H. and Frasca M., Pinning control of chimera states on nonlocal hyperrings. In preparation.
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