26,215 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
Forest structure, stand composition, and climate-growth response in montane forests of Jiuzhaigou National Nature Reserve, China.
Montane forests of western China provide an opportunity to establish baseline studies for climate change. The region is being impacted by climate change, air pollution, and significant human impacts from tourism. We analyzed forest stand structure and climate-growth relationships from Jiuzhaigou National Nature Reserve in northwestern Sichuan province, along the eastern edge of the Tibetan plateau. We conducted a survey to characterize forest stand diversity and structure in plots occurring between 2050 and 3350 m in elevation. We also evaluated seedling and sapling recruitment and tree-ring data from four conifer species to assess: 1) whether the forest appears in transition toward increased hardwood composition; 2) if conifers appear stressed by recent climate change relative to hardwoods; and 3) how growth of four dominant species responds to recent climate. Our study is complicated by clear evidence of 20(th) century timber extraction. Focusing on regions lacking evidence of logging, we found a diverse suite of conifers (Pinus, Abies, Juniperus, Picea, and Larix) strongly dominate the forest overstory. We found population size structures for most conifer tree species to be consistent with self-replacement and not providing evidence of shifting composition toward hardwoods. Climate-growth analyses indicate increased growth with cool temperatures in summer and fall. Warmer temperatures during the growing season could negatively impact conifer growth, indicating possible seasonal climate water deficit as a constraint on growth. In contrast, however, we found little relationship to seasonal precipitation. Projected warming does not yet have a discernible signal on trends in tree growth rates, but slower growth with warmer growing season climates suggests reduced potential future forest growth
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