131 research outputs found
Reproducibility of a noisy limit-cycle oscillator induced by a fluctuating input
Reproducibility of a noisy limit-cycle oscillator driven by a random
piecewise constant signal is analyzed. By reducing the model to random phase
maps, it is shown that the reproducibility of the limit cycle generally
improves when the phase maps are monotonically increasing.Comment: 4 pages, 3 figures, Prog. Theoret. Phys. Suppl. 200
Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson
impulses shows a range of non-trivial behavior, from synchronization,
desynchronization, to clustering. The group behavior that arises in the
ensemble can be predicted from the phase response of a single oscillator to a
given impulsive perturbation. We present a theory based on phase reduction of a
jump stochastic process describing a Poisson-driven limit-cycle oscillator, and
verify the results through numerical simula- tions and electric circuit
experiments. We also give a geometrical interpretation of the synchronizing
mechanism, a perturbative expansion to the stationary phase distribution, and
the diffusion limit of our jump stochastic model
A common goodness-of-fit framework for neural population models using marked point process time-rescaling
A critical component of any statistical modeling procedure is the ability to assess the goodness-of-fit between a model and observed data. For spike train models of individual neurons, many goodness-of-fit measures rely on the time-rescaling theorem and assess model quality using rescaled spike times. Recently, there has been increasing interest in statistical models that describe the simultaneous spiking activity of neuron populations, either in a single brain region or across brain regions. Classically, such models have used spike sorted data to describe relationships between the identified neurons, but more recently clusterless modeling methods have been used to describe population activity using a single model. Here we develop a generalization of the time-rescaling theorem that enables comprehensive goodness-of-fit analysis for either of these classes of population models. We use the theory of marked point processes to model population spiking activity, and show that under the correct model, each spike can be rescaled individually to generate a uniformly distributed set of events in time and the space of spike marks. After rescaling, multiple well-established goodness-of-fit procedures and statistical tests are available. We demonstrate the application of these methods both to simulated data and real population spiking in rat hippocampus. We have made the MATLAB and Python code used for the analyses in this paper publicly available through our Github repository at https://github.com/Eden-Kramer-Lab/popTRT.This work was supported by grants from the NIH (MH105174, NS094288) and the Simons Foundation (542971). (MH105174 - NIH; NS094288 - NIH; 542971 - Simons Foundation)Published versio
Collective Phase Sensitivity
The collective phase response to a macroscopic external perturbation of a
population of interacting nonlinear elements exhibiting collective oscillations
is formulated for the case of globally-coupled oscillators. The macroscopic
phase sensitivity is derived from the microscopic phase sensitivity of the
constituent oscillators by a two-step phase reduction. We apply this result to
quantify the stability of the macroscopic common-noise induced synchronization
of two uncoupled populations of oscillators undergoing coherent collective
oscillations.Comment: 6 pages, 3 figure
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
Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses
Populations of uncoupled limit-cycle oscillators receiving common random
impulses show various types of phase-coherent states, which are characterized
by the distribution of phase differences between pairs of oscillators. We
develop a theory to predict the stationary distribution of pairwise phase
difference from the phase response curve, which quantitatively encapsulates the
oscillator dynamics, via averaging of the Frobenius-Perron equation describing
the impulse-driven oscillators. The validity of our theory is confirmed by
direct numerical simulations using the FitzHugh-Nagumo neural oscillator
receiving common Poisson impulses as an example
Collective dynamical response of coupled oscillators with any network structure
We formulate a reduction theory that describes the response of an oscillator
network as a whole to external forcing applied nonuniformly to its constituent
oscillators. The phase description of multiple oscillator networks coupled
weakly is also developed. General formulae for the collective phase sensitivity
and the effective phase coupling between the oscillator networks are found. Our
theory is applicable to a wide variety of oscillator networks undergoing
frequency synchronization. Any network structure can systematically be treated.
A few examples are given to illustrate our theory.Comment: 4 pages, 2 figure
Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
We theoretically investigate collective phase synchronization between
interacting groups of globally coupled noisy identical phase oscillators
exhibiting macroscopic rhythms. Using the phase reduction method, we derive
coupled collective phase equations describing the macroscopic rhythms of the
groups from microscopic Langevin phase equations of the individual oscillators
via nonlinear Fokker-Planck equations. For sinusoidal microscopic coupling, we
determine the type of the collective phase coupling function, i.e., whether the
groups exhibit in-phase or anti-phase synchronization. We show that the
macroscopic rhythms can exhibit effective anti-phase synchronization even if
the microscopic phase coupling between the groups is in-phase, and vice versa.
Moreover, near the onset of collective oscillations, we analytically obtain the
collective phase coupling function using center-manifold and phase reductions
of the nonlinear Fokker-Planck equations.Comment: 15 pages, 7 figure
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