17,200 research outputs found
Capturing pattern bi-stability dynamics in delay-coupled swarms
Swarms of large numbers of agents appear in many biological and engineering
fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been
observed in many models of large population swarms. However, many reduced
models for analysis, such as mean-field (MF), do not capture the bifurcation
structure of bi-stable behavior. Here, we develop a new model for the dynamics
of a large population swarm with delayed coupling. The additional physics
predicts how individual particle dynamics affects the motion of the entire
swarm. Specifically, (1) we correct the center of mass propulsion physics
accounting for the particles velocity distribution; (2) we show that the model
we develop is able to capture the pattern bi-stability displayed by the full
swarm model.Comment: 6 pages 4 figure
Noise, Bifurcations, and Modeling of Interacting Particle Systems
We consider the stochastic patterns of a system of communicating, or coupled,
self-propelled particles in the presence of noise and communication time delay.
For sufficiently large environmental noise, there exists a transition between a
translating state and a rotating state with stationary center of mass. Time
delayed communication creates a bifurcation pattern dependent on the coupling
amplitude between particles. Using a mean field model in the large number
limit, we show how the complete bifurcation unfolds in the presence of
communication delay and coupling amplitude. Relative to the center of mass, the
patterns can then be described as transitions between translation, rotation
about a stationary point, or a rotating swarm, where the center of mass
undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of
some of the stochastic patterns will be given for large numbers of particles
Statistical multi-moment bifurcations in random delay coupled swarms
We study the effects of discrete, randomly distributed time delays on the
dynamics of a coupled system of self-propelling particles. Bifurcation analysis
on a mean field approximation of the system reveals that the system possesses
patterns with certain universal characteristics that depend on distinguished
moments of the time delay distribution. Specifically, we show both
theoretically and numerically that although bifurcations of simple patterns,
such as translations, change stability only as a function of the first moment
of the time delay distribution, more complex patterns arising from Hopf
bifurcations depend on all of the moments
Enhancing noise-induced switching times in systems with distributed delays
The paper addresses the problem of calculating the noise-induced switching rates in systems with
delay-distributed kernels and Gaussian noise. A general variational formulation for the switching
rate is derived for any distribution kernel, and the obtained equations of motion and boundary conditions
represent the most probable, or optimal, path, which maximizes the probability of escape.
Explicit analytical results for the switching rates for small mean time delays are obtained for the
uniform and bi-modal (or two-peak) distributions. They suggest that increasing the width of the distribution
leads to an increase in the switching times even for longer values of mean time delays for
both examples of the distribution kernel, and the increase is higher in the case of the two-peak distribution.
Analytical predictions are compared to the direct numerical simulations and show excellent
agreement between theory and numerical experiment
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