huepe2011adaptivenetwork
Adaptive-network models of swarm dynamics
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 non-spatial model suggests that spatial geometry may have a lesser impact on collective motion than previously thought.
![Bifurcation diagram of the density of right-going locusts \([R]\) versus link creation rate \(a_{\rm o}\). Solutions of the ODE system of equations (1)–(3) (solid line) yield a supercritical pitchfork bifurcation in excellent agreement with the results from numerical network simulations (circles). Bottom: phase diagram showing the bifurcation point as a function of the link creation rates \(a_{\rm o}\) and \(a_{\rm e}\). In the bistable region (grey), the pitchfork bifurcation becomes subcritical.](https://biond.org/files/upload/figure/AA5Gy1rUqS9h.jpg)
Figure 1: Bifurcation diagram of the density of right-going locusts \([R]\) versus link creation rate \(a_{\rm o}\). Solutions of the ODE system of equations (1)–(3) (solid line) yield a supercritical pitchfork bifurcation in excellent agreement with the results from numerical network simulations (circles). Bottom: phase diagram showing the bifurcation point as a function of the link creation rates \(a_{\rm o}\) and \(a_{\rm e}\). In the bistable region (grey), the pitchfork bifurcation becomes subcritical.