167 research outputs found
Asymptotic absorption-time distributions in extinction-prone Markov processes
We characterize absorption-time distributions for birth-death Markov chains
with an absorbing boundary. For "extinction-prone" chains (which drift on
average toward the absorbing state) the asymptotic distribution is Gaussian,
Gumbel, or belongs to a family of skewed distributions. The latter two cases
arise when the dynamics slow down dramatically near the boundary. Several
models of evolution, epidemics, and chemical reactions fall into these classes;
in each case we establish new results for the absorption-time distribution.
Applications to African sleeping sickness are discussed.Comment: 6 pages, 4 figures, 11 page supplemental materia
Kuramoto model with coupling through an external medium
Synchronization of coupled oscillators is often described using the Kuramoto
model. Here we study a generalization of the Kuramoto model where oscillators
communicate with each other through an external medium. This generalized model
exhibits interesting new phenomena such as bistability between synchronization
and incoherence and a qualitatively new form of synchronization where the
external medium exhibits small-amplitude oscillations. We conclude by
discussing the relationship of the model to other variations of the Kuramoto
model including the Kuramoto model with a bimodal frequency distribution and
the Millennium Bridge problem.Comment: 9 pages, 3 figure
Evolutionary game dynamics of controlled and automatic decision-making
We integrate dual-process theories of human cognition with evolutionary game
theory to study the evolution of automatic and controlled decision-making
processes. We introduce a model where agents who make decisions using either
automatic or controlled processing compete with each other for survival. Agents
using automatic processing act quickly and so are more likely to acquire
resources, but agents using controlled processing are better planners and so
make more effective use of the resources they have. Using the replicator
equation, we characterize the conditions under which automatic or controlled
agents dominate, when coexistence is possible, and when bistability occurs. We
then extend the replicator equation to consider feedback between the state of
the population and the environment. Under conditions where having a greater
proportion of controlled agents either enriches the environment or enhances the
competitive advantage of automatic agents, we find that limit cycles can occur,
leading to persistent oscillations in the population dynamics. Critically,
however, these limit cycles only emerge when feedback occurs on a sufficiently
long time scale. Our results shed light on the connection between evolution and
human cognition, and demonstrate necessary conditions for the rise and fall of
rationality.Comment: 9 pages, 7 figure
Scaling and singularities in the entrainment of globally-coupled oscillators
The onset of collective behavior in a population of globally coupled
oscillators with randomly distributed frequencies is studied for phase
dynamical models with arbitrary coupling. The population is described by a
Fokker-Planck equation for the distribution of phases which includes the
diffusive effect of noise in the oscillator frequencies. The bifurcation from
the phase-incoherent state is analyzed using amplitude equations for the
unstable modes with particular attention to the dependence of the nonlinearly
saturated mode on the linear growth rate . In general
we find where is the
diffusion coefficient and is the mode number of the unstable mode. The
unusual factor arises from a singularity in the cubic term of
the amplitude equation.Comment: 11 pages (Revtex); paper submitted to Phys. Rev. Let
Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode
An amplitude equation for an unstable mode in a collisionless plasma is
derived from the dynamics on the two-dimensional unstable manifold of the
equilibrium. The mode amplitude decouples from the phase due to the
spatial homogeneity of the equilibrium, and the resulting one-dimensional
dynamics is analyzed using an expansion in . As the linear growth rate
vanishes, the expansion coefficients diverge; a rescaling
of the mode amplitude absorbs these
singularities and reveals that the mode electric field exhibits trapping
scaling as . The dynamics for
depends only on the phase where is the derivative of the dielectric as
.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the
Author ([email protected]); paper accepted by Physical Review
Letter
Design and fabrication of a nonlinear micro impact oscillator
In this paper we describe the design and fabrication of a mechanical autonomous impact oscillator with a MEMS resonator as the frequency control element. The design has been developed with scalability to large 2-D arrays of coupled oscillators in mind. The dynamic behaviour of the impact oscillator was numerically studied and it was found that the geometry nonlinearity has an effect on the static pull-in voltage and equilibrium position. The external driving power can alter the frequency of the impact oscillator. The autonomous nature of the oscillator simplifies the complexity of the drive circuitry and is essential for large 2-D arrays
A linear reformulation of the Kuramoto model of self-synchronizing oscillators
The present paper introduces a linear reformulation of the Kuramoto model
describing a self-synchronizing phase transition in a system of globally
coupled oscillators that in general have different characteristic frequencies.
The reformulated model provides an alternative coherent framework through which
one can analytically tackle synchronization problems that are not amenable to
the original Kuramoto analysis. It allows one to solve explicitly for the
synchronization order parameter and the critical point of 1) the full
phase-locking transition for a system with a finite number of oscillators
(unlike the original Kuramoto model, which is solvable implicitly only in the
mean-field limit) and 2) a new class of continuum systems. It also makes it
possible to probe the system's dynamics as it moves towards a steady state.
While discussion in this paper is restricted to systems with global coupling,
the new formalism introduced by the linear reformulation also lends itself to
solving systems that exhibit local or asymmetric coupling.Comment: Accepted to Phys. Rev. E. v5: Further clarified terminology; expanded
discussion; added reference
Predator-Prey Quasi-cycles from a Path Integral Formalism
The existence of beyond mean field quasi-cycle oscillations in a simple
spatial model of predator prey interactions is derived from a path integral
formalism. The results agree substantially with those obtained from analysis of
similar models using system size expansions of the master equation. In all of
these analyses, the discrete nature of predator prey populations and finite
size effects lead to persistent oscillations in time, but spatial patterns fail
to form. The path integral formalism goes beyond mean field theory and provides
a focus on individual realizations of the stochastic time evolution of
population not captured in the standard master equation approach.Comment: 4 page
Association between maternal education and infant diarrhea in different household and community environments of Cebu, Philippines
Maternal education is one of the strongest determinants of infant survival in developing countries, however, questions remain regarding the extent to which its effects vary as a function of contextual variables.In this study, a multi-level interactive model is used to assess whether the protective effect of maternal education on the risk of infant diarrhea is modified by three aspects of the mother's familial and community environment: household assets, community economic resources and the availability of mother's clubs. 2484 study participants were interviewed in 1984 as part of the Cebu Longitudinal Infant Health and Nutrition Study.The findings suggest that the protective effect of maternal education on infant diarrhea varies according to the socio-economic environment in which the mother lives: maternal education protects against infant diarrhea in the more economically and socially advantaged communities but has no effect in the more disadvantaged communities. The results also indicate that the protective effect of maternal education is smaller in the wealthier households.These data suggest that improvement in maternal education level, alone, may not always have the expected beneficial effects on infant health. Corollary measures to improve access of mothers and children to basic community resources and efforts to help mothers be more effective in their various social roles may be necessary preconditions for higher levels of maternal education to result in improved infant health.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31922/1/0000875.pd
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