Abstract
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines, requiring a general conceptual framework in order to harvest the potential of these systems. We study the synchronization of coupled oscillators in time-evolving networks defined by the positions of self-propelled agents interacting in real space. In order to understand the impact of mobility in the synchronization process on general grounds, we introduce a simple model of self-propelled hard disks performing persistent random walks in 2$d$ space and carrying an internal Kuramoto phase oscillator. For non-interacting particles, self-propulsion accelerates synchronization. The competition between agent mobility and excluded volume interactions gives rise to a richer scenario, leading to an optimal self-propulsion speed. We identify two extreme dynamic regimes where synchronization can be understood from theoretical considerations. A systematic analysis of our model quantifies the departure from the latter ideal situations and characterizes the different mechanisms leading the evolution of the system. We show that the synchronization of locally coupled mobile oscillators generically proceeds through coarsening verifying dynamic scaling and sharing strong similarities with the phase ordering dynamics of the 2$d$ XY model following a quench. Our results shed light into the generic mechanisms leading the synchronization of mobile agents, providing a efficient way to understand more complex or specific situations involving time-dependent networks where synchronization, mobility and excluded volume are at play.
Highlights
Synchronization processes by which a large population of units spontaneously organize into a cooperative state play an important role in very diverse contexts, from physics to biology going through such disparate fields as ecology, sociology, or neurosciences, among others [1,2]
We present a general framework where the time evolution of the network is self-generated by the stochastic dynamics of physical interacting objects, allowing us to tune the connectivity of the network by changing the coupling range and/or the mobility of the agents, and explore both connected and disconnected structures
The generality of this approach brings a wide range of situations into a unified description, providing access to the universal scenarios generically involved in the synchronization on time-evolving networks
Summary
Synchronization processes by which a large population of units spontaneously organize into a cooperative state play an important role in very diverse contexts, from physics to biology going through such disparate fields as ecology, sociology, or neurosciences, among others [1,2]. The coordinated expression of genetic oscillators, like the segmentation clock, has been shown to play a key role in, for instance, somitogenesis [15] This nonexhaustive list of examples shows that the ability to manipulate and control the synchronization of systems made of mobile entities could be exploited as design principles to build biological sensors, bioinspired materials, or to improve mobile communication systems. In a series of works, Uriu and collaborators introduced lattice models where agents exchange their location at a given rate [22,23,24], as well as a model of phase oscillators attached to repulsive self-propelled particles in closed packed conditions, where the presence of alignment gives rise to an optimal synchronization [25]. Our approach allows us to explore the impact of these dynamical structures, generic in active systems, on the synchronization of phase oscillators, and disentangle the role played by the network structure, self-propulsion, and particle interactions.
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