Time delay can facilitate coherence in self-driven interacting-particle systems

Persistent and responsive collective motion with adaptive time delay

It is beneficial for collective structures to simultaneously have high persistence to environmental noise and high responsivity to nontrivial external stimuli. However, without the ability to differentiate useful information from noise, there is always a tradeoff between persistence and responsivity within the collective structures. To address this, we propose adaptive time delay inspired by the adaptive behavior observed in the school of fish. This strategy is tested using particles powered by optothermal fields coupled with an optical feedback-control system. By applying the adaptive time delay with a proper threshold, we experimentally observe the responsivity of the collective structures enhanced by approximately 1.6 times without sacrificing persistence. Furthermore, we integrate adaptive time delay with long-distance transportation and obstacle-avoidance capabilities to prototype adaptive swarm microrobots. This research demonstrates the potential of adaptive time delay to address the persistence-responsivity tradeoff and lays the foundation for intelligent swarm micro/nanorobots operating in complex environments.

Directional switches in network-organized swarming systems with delay

Coordinated directional switches can emerge between members of moving biological groups. Previous studies have shown that the self-propelled particles model can well reproduce directional switching behaviors, but it neglects the impact of social interactions. Thus, we focus on the influence of social interactions on the ordered directional switching motion of swarming systems, in which homogeneous Erdös-Rényi networks, heterogeneous scale-free networks, networks with community structures, and real-world animal social networks have been considered. The theoretical estimation of mean switching time is obtained, and the results show that the interplay between social and delayed interactions plays an important role in regulating directional switching behavior. To be specific, for homogeneous Erdös-Rényi networks, the increase in mean degree may suppress the directional switching behaviors if the delay is sufficiently small. However, when the delay is large, the large mean degree may promote the directional switching behavior. For heterogeneous scale-free networks, the increase of degree heterogeneity can reduce the mean switching time if the delay is sufficiently small, while the increasing degree heterogeneity may suppress the ordered directional switches if the delay is large. For networks with community structures, higher communities can promote directional switches for small delays, while for large delays, it may inhibit directional switching behavior. For dolphin social networks, delay can promote the directional switching behavior. Our results bring to light the role of social and delayed interactions in the ordered directional switching motion.

Coordinating directional switches in pigeon flocks: the role of nonlinear interactions

The mechanisms inducing unpredictably directional switches in collective and moving biological entities are largely unclear. Deeply understanding such mechanisms is beneficial to delicate design of biologically inspired devices with particular functions. Here, articulating a framework that integrates data-driven, analytical and numerical methods, we investigate the underlying mechanism governing the coordinated rotational flight of pigeon flocks with unpredictably directional switches. Particularly using the sparse Bayesian learning method, we extract the inter-agent interactional dynamics from the high-resolution GPS data of three pigeon flocks, which reveals that the decision-making process in rotational switching flight performs in a more nonlinear manner than in smooth coordinated flight. To elaborate the principle of this nonlinearity of interactions, we establish a data-driven particle model with two potential wells and estimate the mean switching time of rotational direction. Our model with its analytical and numerical results renders the directional switches of moving biological groups more interpretable and predictable. Actually, an appropriate combination of natures, including high density, stronger nonlinearity in interactions, and moderate strength of noise, can enhance such highly ordered, less frequent switches.

Dynamics of the impact of Twitter with time delay on the spread of infectious diseases

In this paper, a mathematical model to study the impact of Twitter in controlling infectious disease is proposed. The model includes the dynamics of “tweets” which may enhance awareness of the disease and cause behavioral changes among the public, thus reducing the transmission of the disease. Furthermore, the model is improved by introducing a time delay between the outbreak of disease and the release of Twitter messages. The basic reproduction number and the conditions for the stability of the equilibria are derived. It is shown that the system undergoes Hopf bifurcation when time delay is increased. Finally, numerical simulations are given to verify the analytical results.

A positive role of multiplicative noise on the emergence of flocking in a stochastic Cucker-Smale system

In this article, we investigate the flocking of a stochastic Cucker-Smale system with multiplicative measurement noise. We show that there is a noise strength, below which the flocking occurs and the convergence time is a decreasing function of noise strength. Specifically, we find a power-law relationship between the convergence time and the density of group. We also investigate the influence of control parameter and an optimal value is found that minimizes the convergence time.