Explosive synchronization in network of mobile oscillators

The role of cellular active stresses in shaping the zebrafish body axis.

Spatial groups and cyclic oscillations induced by positive correlation between moving direction and phase of mobile oscillators

Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling. The transition behaviors are discussed in terms of the timescales of synchronization and diffusion of the oscillators. We also find a novel spatiotemporal pattern at the border between coherent and incoherent states. 

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Effect of mobility on collective phase dynamics of nonlocally coupled oscillators with a phase lag

In this work we bring out the existence of a novel kind of synchronization associated to the size of a complex system. A dichotomic random jump process associated to the dynamics of an externally driven stochastic system with $N$ coupled units is constructed. We define an output frequency and phase diffusion coefficient. System size synchronization occurs when the average output frequency is locked to the external one and the average phase diffusion coefficient shows a very deep minimum for a range of system sizes. Analytical and numerical procedures are introduced to study the phenomenon, and the results describe successfully the existence of system size synchronization.

System size synchronization

Individual biological oscillators can synchronize to generate a collective rhythm. During vertebrate development, mobile cells exchange signals to synchronize a rhythmic pattern generator that makes the embryonic segments. Previous theoretical works have shown that cell mobility can enhance synchronization of coupled oscillators when signal exchange is instantaneous. However, in vertebrate segmentation, the exchange of signals is thought to comprise delays from signal sending and processing, which could alter the effect of mobility on synchronization. Here, we study synchronization dynamics of mobile phase oscillators in the presence of coupling delays. We find that mobility can speed up synchronization when coupling delays are present. We derive an analytical expression for the characteristic time of synchronization dynamics, which is in very good agreement with numerical simulations. This analytical expression suggests a subdivision of the mobility range into different dynamical regimes and reveals that, with delayed coupling, synchronization is enhanced at a lower mobility rate than with instantaneous coupling. We argue that these results may be relevant to the synchronization of mobile oscillators in vertebrate segmentation.

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Synchronization dynamics of mobile oscillators in the presence of coupling delays

Antibiotic resistance: Insights from evolution experiments and mathematical modeling

Antibiotic resistance is a growing public health problem. To gain a fundamental understanding of resistance evolution, a combination of systematic experimental and theoretical approaches is required. Evolution experiments combined with next-generation sequencing techniques, laboratory automation, and mathematical modeling are enabling the investigation of resistance development at an unprecedented level of detail. Recent work has directly tracked the intricate stochastic dynamics of bacterial populations in which resistant mutants emerge and compete. In addition, new approaches have enabled measuring how prone a large number of genetically perturbed strains are to evolve resistance. Based on advances in quantitative cell physiology, predictive theoretical models of resistance are increasingly being developed. Taken together, a new strategy for observing, predicting, and ultimately controlling resistance evolution is emerging.

Gabriela Petrungaro

Papers

Synchronization dynamics of mobile oscillators in the presence of coupling delays

Antibiotic resistance: Insights from evolution experiments and mathematical modeling

Antibiotic resistance: Insights from evolution experiments and mathematical modeling.