Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization

Abstract

In this work we revisit the nonmonotonic behavior (NMB) of synchronization time with velocity reported for systems of mobile pulse-coupled oscillators (PCOs). We devise a control parameter that allows us to predict in which range of velocities NMB may occur, also uncovering the conditions allowing us to establish the emergence of NMB based on specific features of the connectivity rule. Specifically, our results show that if the connectivity rule is such that the interaction patterns are sparse and, more importantly, include a large fraction of nonreciprocal interactions, then the system will display NMB. We furthermore provide a microscopic explanation relating the presence of such features of the connectivity patterns to the existence of local clusters unable to synchronize, termed frustrated clusters, for which we also give a precise definition in terms of simple graph concepts. We conclude that, if the probability of finding a frustrated cluster in a system of moving PCOs is high enough, NMB occurs in a predictable range of velocities.

Synchronization dynamics of mobile oscillators in the presence of coupling delays

“…In contrast, in the mouse segmentation clock it is thought that single cells behave as excitable systems [51]. Such excitable systems would require a different description for mobile interacting agents, like that of pulse-coupled mobile oscillators [40,41]. It remains an interesting open question how mobility affects synchronization in the mouse segmentation clock, where coupling delays are also present [19,52].…”

“…The enhancement of synchronization by mobility may occur even in the presence of gradually recovering intercellular interactions [31] and short-range velocity correlations between cells in the tissue [37]. Aside from vertebrate somitogenesis, it has been shown that faster synchronization also occurs for mobile chaotic oscillators [38,39] and moving integrate and fire oscillators [40,41]. The role of mobility as an enhancer of global order in spatially extended systems has also been highlighted in the context of biodiversity [42,43] and social consensus [44].…”

Emergence of synchronization in multiplex networks of mobile Rössler oscillators

“…Here, we are considering square shaped vision sizes in the direction of the motion of the nodes which is simple to understand and fits well with our on-grid platform of the node movement in case of a 2D-lattice random walk. It could have been chosen in other shapes like that of circular or cone shaped vision sizes that has been dealt with in [69][70][71]. But such vision sizes would not allow one to maintain a lattice random walk.…”

Disorder fosters chimera in an array of motile particles

“…For example, for locally coupled phase oscillators randomly moving on one-dimensional lattice [7], motility has been shown to promote a synchronous state. For two-dimensional motions, the authors of [10] observed that there is a resonance range of random velocities, for which the transition to synchrony is extremely slow. The authors of [11] explored one-dimensional lattice with local delayed coupling, the motion of particles was modeled by random exchanges of positions of nearest neighbors; in this setup, a persistent chimera was observed in some range of parameters.…”