On effective temperature in network models of collective behavior

Flocking dynamics mediated by weighted social networks

We study the effects of animal social networks with a weighted pattern of interactions on the flocking transition exhibited by models of self-organized collective motion. We consider variations of traditional models of collective motion in which interactions between individuals are mediated by static complex weighted networks, representing patterns of social interactions. For a model representing dynamics on a one-dimensional substrate, application of a heterogeneous mean-field theory provides a phase diagram as function of the heterogeneity of the network connections and the correlations between weights and degree. In this diagram we observe two phases, one corresponding to the presence of a transition and other to a transition suppressed in an always ordered system, already observed in the nonweighted case. Interestingly, a third phase, with no transition in an always disordered state, is also obtained. These predictions, numerically recovered in computer simulations, are also fulfilled for the more realistic Vicsek model, with movement in a two-dimensional space. Additionally, we observe at finite network sizes the presence of a maximum threshold for particular weight configurations, indicating that it is possible to tune weights to achieve a maximum resilience to noise effects. Simulations in real weighted animal social networks show that, in general, the presence of weights diminishes the value of the flocking threshold, thus increasing the fragility of the flocking state. The shift in the threshold is observed to depend on the heterogeneity of the weight pattern.

Interaction network effects on position- and velocity-based models of collective motion

We study how the structure of the interaction network affects self-organized collective motion in two minimal models of self-propelled agents: the Vicsek model and the Active-Elastic (AE) model. We perform simulations with topologies that interpolate between a nearest-neighbour network and random networks with different degree distributions to analyse the relationship between the interaction topology and the resilience to noise of the ordered state. For the Vicsek case, we find that a higher fraction of random connections with homogeneous or power-law degree distribution increases the critical noise, and thus the resilience to noise, as expected due to small-world effects. Surprisingly, for the AE model, a higher fraction of random links with power-law degree distribution can decrease this resilience, despite most links being long-range. We explain this effect through a simple mechanical analogy, arguing that the larger presence of agents with few connections contributes localized low-energy modes that are easily excited by noise, thus hindering the collective dynamics. These results demonstrate the strong effects of the interaction topology on self-organization. Our work suggests potential roles of the interaction network structure in biological collective behaviour and could also help improve decentralized swarm robotics control and other distributed consensus systems.

A statistical physics view of swarming bacteria

Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.

Kinetic order-disorder transitions in a pause-and-go swarming model with memory

A two dimensional model of self-propelled particles combining both a pause-and-go movement pattern and memory is studied in simulations. It is shown, that in contrast to previously studied agent based models in two-dimensions, order and disorder are metastable states that can co-exist at some parameter range. In particular, this implies that the formation and decay of global order in swarms may be kinetic rather than a phase transition. Our results explain metastability recently observed in swarming locust and fish.

Interaction between synchronization and motion in a system of mobile agents

In this paper, we study synchronization in time-varying networks inherited by the Vicsek's model of self-propelled particles. In our model, each particle/agent moves in a two dimensional space according to the Vicsek's rules and is associated to a chaotic system. The dynamics of two oscillators are coupled with each other only when agents are at a distance less than an interaction radius. We investigate the system behavior with respect to some fundamental parameters, and, in particular, to the noise level, which for increasing intensity drives the system from an ordered motion to a disordered one. We show that the global dynamics is ruled by the interplay between motion characteristics and dynamical coupling with synchronization either favored or inhibited by a coordinated motion of the self-propelled particles. Finally, we provide semi-analytical estimation for the synchronization thresholds for interconnections occurring at a time-scale shorter than that of the associated dynamical systems.