Adaptive-network models of swarm dynamics

Abstract

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical investigation. We find that the model reproduces several characteristic features of swarms, including spontaneous symmetry breaking, noise-and density-driven order-disorder transitions that can be of first or second order, and intermittency. Reproducing these experimental observations using a nonspatial model suggests that spatial geometry may have a lesser impact on collective motion than previously thought.

Swarming on Random Graphs

“…In robotics, for instance, all-to-all communication can prove prohibitively expensive for a large number of robots. Related models also frequently demand a theoretical understanding how a (possibly dynamic) random network interaction structure affects well-understood, deterministic behaviors such as phase transitions [1], consensus and synchronization [26,31], and the emergence of collective behavior in locust swarms [18]. Thus it is quite relevant to understand the stability of such system properties in the presence of a relatively sparse network or a random interaction topology.…”

Network inoculation: Heteroclinics and phase transitions in an epidemic model

“…The transcritical bifurcation and its close relatives, the fold and pitchfork bifurcations have been linked to phase transitions in a wide variety of systems including epidemics 4 , collective motion of animals 6,7 , human opinion formation 8,9 , neuronal dynamics 10,11 and others. In a smaller number of models the underlying bifurcation is a Hopf bifurcation, which marks the onset of, at least transient, oscillations [12][13][14] .…”

Promoting collective motion of self-propelled agents by distance-based influence

“…In recent years, a variety of efforts have been devoted to modeling the dynamic properties of swarms [15][16][17][18][19][20][21][22][23][24][25][26][27]. In 1995, Vicsek et al proposed a particularly simple but rich model [28].…”