44 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
Coherent Pattern Prediction in Swarms of Delay-Coupled Agents
We consider a general swarm model of self-propelling agents interacting
through a pairwise potential in the presence of noise and communication time
delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a
communication time delay in the swarm induces a pattern bifurcation that
depends on the size of the coupling amplitude. We extend these results by
completely unfolding the bifurcation structure of the mean field approximation.
Our analysis reveals a direct correspondence between the different dynamical
behaviors found in different regions of the coupling-time delay plane with the
different classes of simulated coherent swarm patterns. We derive the
spatio-temporal scales of the swarm structures, and also demonstrate how the
complicated interplay of coupling strength, time delay, noise intensity, and
choice of initial conditions can affect the swarm. In particular, our studies
show that for sufficiently large values of the coupling strength and/or the
time delay, there is a noise intensity threshold that forces a transition of
the swarm from a misaligned state into an aligned state. We show that this
alignment transition exhibits hysteresis when the noise intensity is taken to
be time dependent
Intervention-Based Stochastic Disease Eradication
Disease control is of paramount importance in public health with infectious
disease extinction as the ultimate goal. Although diseases may go extinct due
to random loss of effective contacts where the infection is transmitted to new
susceptible individuals, the time to extinction in the absence of control may
be prohibitively long. Thus intervention controls, such as vaccination of
susceptible individuals and/or treatment of infectives, are typically based on
a deterministic schedule, such as periodically vaccinating susceptible children
based on school calendars. In reality, however, such policies are administered
as a random process, while still possessing a mean period. Here, we consider
the effect of randomly distributed intervention as disease control on large
finite populations. We show explicitly how intervention control, based on mean
period and treatment fraction, modulates the average extinction times as a
function of population size and rate of infection spread. In particular, our
results show an exponential improvement in extinction times even though the
controls are implemented using a random Poisson distribution. Finally, we
discover those parameter regimes where random treatment yields an exponential
improvement in extinction times over the application of strictly periodic
intervention. The implication of our results is discussed in light of the
availability of limited resources for control.Comment: 18 pages, 10 Figure
The Origins of Time-Delay in Template Biopolymerization Processes
Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models