1,114 research outputs found
Cooperative behavior between oscillatory and excitable units: the peculiar role of positive coupling-frequency correlations
We study the collective dynamics of noise-driven excitable elements,
so-called active rotators. Crucially here, the natural frequencies and the
individual coupling strengths are drawn from some joint probability
distribution. Combining a mean-field treatment with a Gaussian approximation
allows us to find examples where the infinite-dimensional system is reduced to
a few ordinary differential equations. Our focus lies in the cooperative
behavior in a population consisting of two parts, where one is composed of
excitable elements, while the other one contains only self-oscillatory units.
Surprisingly, excitable behavior in the whole system sets in only if the
excitable elements have a smaller coupling strength than the self-oscillating
units. In this way positive local correlations between natural frequencies and
couplings shape the global behavior of mixed populations of excitable and
oscillatory elements.Comment: 10 pages, 6 figures, published in Eur. Phys. J.
Time-delayed feedback in neurosystems
The influence of time delay in systems of two coupled excitable neurons is
studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in
the coupling between neurons or in a self-feedback loop. The stochastic
synchronization of instantaneously coupled neurons under the influence of white
noise can be deliberately controlled by local time-delayed feedback. By
appropriate choice of the delay time synchronization can be either enhanced or
suppressed. In delay-coupled neurons, antiphase oscillations can be induced for
sufficiently large delay and coupling strength. The additional application of
time-delayed self-feedback leads to complex scenarios of synchronized in-phase
or antiphase oscillations, bursting patterns, or amplitude death.Comment: 13 pages, 13 figure
Shaping bursting by electrical coupling and noise
Gap-junctional coupling is an important way of communication between neurons
and other excitable cells. Strong electrical coupling synchronizes activity
across cell ensembles. Surprisingly, in the presence of noise synchronous
oscillations generated by an electrically coupled network may differ
qualitatively from the oscillations produced by uncoupled individual cells
forming the network. A prominent example of such behavior is the synchronized
bursting in islets of Langerhans formed by pancreatic \beta-cells, which in
isolation are known to exhibit irregular spiking. At the heart of this
intriguing phenomenon lies denoising, a remarkable ability of electrical
coupling to diminish the effects of noise acting on individual cells.
In this paper, we derive quantitative estimates characterizing denoising in
electrically coupled networks of conductance-based models of square wave
bursting cells. Our analysis reveals the interplay of the intrinsic properties
of the individual cells and network topology and their respective contributions
to this important effect. In particular, we show that networks on graphs with
large algebraic connectivity or small total effective resistance are better
equipped for implementing denoising. As a by-product of the analysis of
denoising, we analytically estimate the rate with which trajectories converge
to the synchronization subspace and the stability of the latter to random
perturbations. These estimates reveal the role of the network topology in
synchronization. The analysis is complemented by numerical simulations of
electrically coupled conductance-based networks. Taken together, these results
explain the mechanisms underlying synchronization and denoising in an important
class of biological models
Mean field approximation of two coupled populations of excitable units
The analysis on stability and bifurcations in the macroscopic dynamics
exhibited by the system of two coupled large populations comprised of
stochastic excitable units each is performed by studying an approximate system,
obtained by replacing each population with the corresponding mean-field model.
In the exact system, one has the units within an ensemble communicating via the
time-delayed linear couplings, whereas the inter-ensemble terms involve the
nonlinear time-delayed interaction mediated by the appropriate global
variables. The aim is to demonstrate that the bifurcations affecting the
stability of the stationary state of the original system, governed by a set of
4N stochastic delay-differential equations for the microscopic dynamics, can
accurately be reproduced by a flow containing just four deterministic
delay-differential equations which describe the evolution of the mean-field
based variables. In particular, the considered issues include determining the
parameter domains where the stationary state is stable, the scenarios for the
onset and the time-delay induced suppression of the collective mode, as well as
the parameter domains admitting bistability between the equilibrium and the
oscillatory state. We show how analytically tractable bifurcations occurring in
the approximate model can be used to identify the characteristic mechanisms by
which the stationary state is destabilized under different system
configurations, like those with symmetrical or asymmetrical inter-population
couplings.Comment: 5 figure
Synchronization of coupled neural oscillators with heterogeneous delays
We investigate the effects of heterogeneous delays in the coupling of two
excitable neural systems. Depending upon the coupling strengths and the time
delays in the mutual and self-coupling, the compound system exhibits different
types of synchronized oscillations of variable period. We analyze this
synchronization based on the interplay of the different time delays and support
the numerical results by analytical findings. In addition, we elaborate on
bursting-like dynamics with two competing timescales on the basis of the
autocorrelation function.Comment: 18 pages, 14 figure
Synchronization induced by periodic inputs in finite -unit bistable Langevin models: The augmented moment method
We have studied the synchronization induced by periodic inputs applied to the
finite -unit coupled bistable Langevin model which is subjected to
cross-correlated additive and multiplicative noises. Effects on the
synchronization of the system size (), the coupling strength and the
cross-correlation between additive and multiplicative noises have been
investigated with the use of the semi-analytical augmented moment method (AMM)
which is the second-order moment approximation for local and global variables
[H. Hasegawa, Phys. Rev. E {\bf 67} (2003) 041903]. A linear analysis of the
stationary solution of AMM equations shows that the stability is improved
(degraded) by positive (negative) couplings. Results of the nonlinear bistable
Langevin model are compared to those of the linear Langevin model.Comment: 19 pages, 10 figures, the final version with a changed title,
accepted in Physica
Synchronised firing induced by network dynamics in excitable systems
We study the collective dynamics of an ensemble of coupled identical
FitzHugh--Nagumo elements in their excitable regime. We show that collective
firing, where all the elements perform their individual firing cycle
synchronously, can be induced by random changes in the interaction pattern.
Specifically, on a sparse evolving network where, at any time, each element is
connected with at most one partner, collective firing occurs for intermediate
values of the rewiring frequency. Thus, network dynamics can replace noise and
connectivity in inducing this kind of self-organised behaviour in highly
disconnected systems which, otherwise, wouldn't allow for the spreading of
coherent evolution.Comment: 5 pages, 5 figure
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