Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching

By Per Sebastian Skardal, Alex Arenas. Communications Physics, 2019

339 citations recorded by the source corpus.

Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units, i.e., three- and four-way interactions in addition to pairwise interactions, and their role in shaping collective behavior. Here we show that higher-order interactions between coupled phase oscillators, encoded microscopically in a simplicial complex, give rise to added nonlinearity in the macroscopic system dynamics that induces abrupt synchronization transitions via hysteresis and bistability of synchronized and incoherent states. Moreover, these higher-order interactions can stabilize strongly synchronized states even when the pairwise coupling is repulsive. These findings reveal a self-organized phenomenon that may be responsible for the rapid switching to synchronization in many biological and other systems that exhibit synchronization without the need of particular correlation mechanisms between the oscillators and the topological structure. While first order phase transitions between incoherence and synchronization are critical for collective behavior in various oscillator system application, e.g., the brain and power grids, such transitions typically require finely tuned properties. In this work the authors show that first order phase transitions and bistability can emerge naturally as a consequence of the presence of higher-order interactions between oscillators.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6c2fe801fa22aee8a98e9d01684e19a20dc409df

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Citations in the corpus

What are higher-order networks? (2021, background): “From this perspective it is not surprising that the same dynamical effect, such as discontinuous synchronization transitions [176], can be observed in coupled nonlinear oscillators without higherorder interactions [85] and phase oscillators with higher-order interactions [259]: The network dynamical”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “[376] remains mathematically tractable because oscillators have identical frequencies.”