Noise Induced Pattern Switching in Randomly Distributed Delayed Swarm Patterns

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the stability of a class of emerging patterns depends upon all moments of the time delay distribution, and predicts their bifurcation parameter ranges. Near the bifurcations of these patterns, noise may induce a transition from one type of pattern to another. We study the onset of these noise-induced swarm re-organizations by numerically simulating the system over a range of noise intensities and for various distributions of the delays. Interestingly, there is a critical noise threshold above which the system is forced to transition from a less organized state to a more organized one. We explore this phenomenon by quantifying this critical noise threshold, and note that transition time between states varies as a function of both the noise intensity and delay distribution.