Control of Synchronization Regimes in Networks of Mobile Interacting Agents

Abstract

We investigate synchronization in a population of mobile pulse-coupled agents with a view towards implementations in swarm-robotics systems and mobile sensor networks. Previous theoretical approaches dealt with range and nearest-neighbor interactions. In the latter case, a synchronization-hindering regime for intermediate agent mobility is found. We investigate the robustness of this intermediate regime under practical scenarios. We show that synchronization in the intermediate regime can be predicted by means of a suitable metric of the phase response curve. Furthermore, we study more-realistic K-nearest-neighbor and cone-of-vision interactions, showing that it is possible to control the extent of the synchronizationhindering region by appropriately tuning the size of the neighborhood. To assess the effect of noise, we analyze the propagation of perturbations over the network and draw an analogy between the response in the hindering regime and stable chaos. Our findings reveal the conditions for the control of clock or activity synchronization of agents with intermediate mobility. In addition, the emergence of the intermediate regime is validated experimentally using a swarm of physical robots interacting with cone-of-vision interactions.

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

“…Similarity between the periods of the units is crucial to achieve such a synchronized state but there is another ingredient that plays also a very significant role: the pattern of interactions between the units [4][5][6]. It is important not only for determining the time scale to reach a stationary state but in some cases-as in the situation under study in the present work-it can even prevent the synchronization of identical units [7,8].…”

“…In particular, more recent works [8,20] have confirmed that a sparse and nonreciprocal interaction pattern is a necessary condition for such behavior to be observed, yet the validity of the general interpretation based on the two time scales has not been verified.…”

“…In this paper, we analyze the model proposed in [8,20], showing how it fits the interpretation proposed in [7]. Additionally, we introduce a general explanation of what the unfruitful interplay between time scales is and how and why it is related to features (a) and (b) of the interaction pattern.…”

“…The worst scenario corresponds to the cluster having almost reached a coherent state when it changes into a frustrated configuration. Because of the peculiar characteristics of the pulse coupling (with small enough refractory period, otherwise NMB does not appear [8]), the achieved partial coherence will be wasted. Conversely, an optimal case would be the one in which a cluster becomes frustrated due to a change in the internal interactions just after synchronizing.…”

“…The model considered in this paper was introduced in [8,20] and can be regarded as a modified version of the minimal model originally proposed in [7]. It consists of a population of N moving oscillators with velocity V and random orientation on a square of side length L with finite boundary conditions.…”