814 research outputs found
Resonance Behavior and Partial Averaging in a Three-Body System with Gravitational Radiation Damping
In a previous investigation, a model of three-body motion was developed which
included the effects of gravitational radiation reaction. The aim was to
describe the motion of a relativistic binary pulsar that is perturbed by a
third mass and look for resonances between the binary and third mass orbits.
Numerical integration of an equation of relative motion that approximates the
binary gives evidence of such resonances. These resonances are defined
for the present purposes by the resonance condition, , where
and are relatively prime integers and and are the
angular frequencies of the binary orbit and third mass orbit, respectively. The
resonance condition consequently fixes a value for the semimajor axis of
the binary orbit for the duration of the resonance because of the Kepler
relationship . This paper outlines a method of averaging
developed by Chicone, Mashhoon, and Retzloff which renders a nonlinear system
that undergoes resonance capture into a mathematically amenable form. This
method is applied to the present system and one arrives at an analytical
solution that describes the average motion during resonance. Furthermore,
prominent features of the full nonlinear system, such as the frequency of
oscillation and antidamping, accord with their analytically derived formulae.Comment: 19 pages, 4 Postscript figure
Investigation of vertical cavity surface emitting laser dynamics for neuromorphic photonic systems
We report an approach based upon vertical cavity surface emitting lasers (VCSELs) to reproduce optically different behaviors exhibited by biological neurons but on a much faster timescale. The technique proposed is based on the polarization switching and nonlinear dynamics induced in a single VCSEL under polarized optical injection. The particular attributes of VCSELs and the simple experimental configuration used in this work offer prospects of fast, reconfigurable processing elements with excellent fan-out and scaling potentials for use in future computational paradigms and artificial neural networks. © 2012 American Institute of Physics
Optimizing periodicity and polymodality in noise-induced genetic oscillators
Many cellular functions are based on the rhythmic organization of biological
processes into self-repeating cascades of events. Some of these periodic
processes, such as the cell cycles of several species, exhibit conspicuous
irregularities in the form of period skippings, which lead to polymodal
distributions of cycle lengths. A recently proposed mechanism that accounts for
this quantized behavior is the stabilization of a Hopf-unstable state by
molecular noise. Here we investigate the effect of varying noise in a model
system, namely an excitable activator-repressor genetic circuit, that displays
this noise-induced stabilization effect. Our results show that an optimal noise
level enhances the regularity (coherence) of the cycles, in a form of coherence
resonance. Similar noise levels also optimize the multimodal nature of the
cycle lengths. Together, these results illustrate how molecular noise within a
minimal gene regulatory motif confers robust generation of polymodal patterns
of periodicity.Comment: 9 pages, 6 figure
The Dynamics of Hybrid Metabolic-Genetic Oscillators
The synthetic construction of intracellular circuits is frequently hindered
by a poor knowledge of appropriate kinetics and precise rate parameters. Here,
we use generalized modeling (GM) to study the dynamical behavior of topological
models of a family of hybrid metabolic-genetic circuits known as
"metabolators." Under mild assumptions on the kinetics, we use GM to
analytically prove that all explicit kinetic models which are topologically
analogous to one such circuit, the "core metabolator," cannot undergo Hopf
bifurcations. Then, we examine more detailed models of the metabolator.
Inspired by the experimental observation of a Hopf bifurcation in a
synthetically constructed circuit related to the core metabolator, we apply GM
to identify the critical components of the synthetically constructed
metabolator which must be reintroduced in order to recover the Hopf
bifurcation. Next, we study the dynamics of a re-wired version of the core
metabolator, dubbed the "reverse" metabolator, and show that it exhibits a
substantially richer set of dynamical behaviors, including both local and
global oscillations. Prompted by the observation of relaxation oscillations in
the reverse metabolator, we study the role that a separation of genetic and
metabolic time scales may play in its dynamics, and find that widely separated
time scales promote stability in the circuit. Our results illustrate a generic
pipeline for vetting the potential success of a potential circuit design,
simply by studying the dynamics of the corresponding generalized model
Numerical Solution of Differential Equations by the Parker-Sochacki Method
A tutorial is presented which demonstrates the theory and usage of the
Parker-Sochacki method of numerically solving systems of differential
equations. Solutions are demonstrated for the case of projectile motion in air,
and for the classical Newtonian N-body problem with mutual gravitational
attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a
university web site, but has now been cited and praised in one or more
refereed journals. I am therefore submitting it to the Cornell arXiv so that
it may be read in response to its citations. See "Spiking neural network
simulation: numerical integration with the Parker-Sochacki method:" J. Comput
Neurosci, Robert D. Stewart & Wyeth Bair and
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378
Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
We study the effects of network topology on the response of networks of
coupled discrete excitable systems to an external stochastic stimulus. We
extend recent results that characterize the response in terms of spectral
properties of the adjacency matrix by allowing distributions in the
transmission delays and in the number of refractory states, and by developing a
nonperturbative approximation to the steady state network response. We confirm
our theoretical results with numerical simulations. We find that the steady
state response amplitude is inversely proportional to the duration of
refractoriness, which reduces the maximum attainable dynamic range. We also
find that transmission delays alter the time required to reach steady state.
Importantly, neither delays nor refractoriness impact the general prediction
that criticality and maximum dynamic range occur when the largest eigenvalue of
the adjacency matrix is unity
Conedy: a scientific tool to investigate Complex Network Dynamics
We present Conedy, a performant scientific tool to numerically investigate
dynamics on complex networks. Conedy allows to create networks and provides
automatic code generation and compilation to ensure performant treatment of
arbitrary node dynamics. Conedy can be interfaced via an internal script
interpreter or via a Python module
GeNN: a code generation framework for accelerated brain simulations
Large-scale numerical simulations of detailed brain circuit models are important for identifying hypotheses on brain functions and testing their consistency and plausibility. An ongoing challenge for simulating realistic models is, however, computational speed. In this paper, we present the GeNN (GPU-enhanced Neuronal Networks) framework, which aims to facilitate the use of graphics accelerators for computational models of large-scale neuronal networks to address this challenge. GeNN is an open source library that generates code to accelerate the execution of network simulations on NVIDIA GPUs, through a flexible and extensible interface, which does not require in-depth technical knowledge from the users. We present performance benchmarks showing that 200-fold speedup compared to a single core of a CPU can be achieved for a network of one million conductance based Hodgkin-Huxley neurons but that for other models the speedup can differ.
GeNN is available for Linux, Mac OS X and Windows platforms. The source code, user manual, tutorials,
Wiki, in-depth example projects and all other related information can be found on the project website http://genn-team.github.io/genn/
Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
We study synchronization properties of general uncoupled limit-cycle
oscillators driven by common and independent Gaussian white noises. Using phase
reduction and averaging methods, we analytically derive the stationary
distribution of the phase difference between oscillators for weak noise
intensity. We demonstrate that in addition to synchronization, clustering, or
more generally coherence, always results from arbitrary initial conditions,
irrespective of the details of the oscillators.Comment: 6 pages, 2 figure
Higher order approximation of isochrons
Phase reduction is a commonly used techinque for analyzing stable
oscillators, particularly in studies concerning synchronization and phase lock
of a network of oscillators. In a widely used numerical approach for obtaining
phase reduction of a single oscillator, one needs to obtain the gradient of the
phase function, which essentially provides a linear approximation of isochrons.
In this paper, we extend the method for obtaining partial derivatives of the
phase function to arbitrary order, providing higher order approximations of
isochrons. In particular, our method in order 2 can be applied to the study of
dynamics of a stable oscillator subjected to stochastic perturbations, a topic
that will be discussed in a future paper. We use the Stuart-Landau oscillator
to illustrate the method in order 2
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