502 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.
Critical phenomena in globally coupled excitable elements
Critical phenomena in globally coupled excitable elements are studied by
focusing on a saddle-node bifurcation at the collective level. Critical
exponents that characterize divergent fluctuations of interspike intervals near
the bifurcation are calculated theoretically. The calculated values appear to
be in good agreement with those determined by numerical experiments. The
relevance of our results to jamming transitions is also mentioned.Comment: 4 pages, 3 figure
Self-Sustaining Oscillations in Complex Networks of Excitable Elements
Random networks of symmetrically coupled, excitable elements can
self-organize into coherently oscillating states if the networks contain loops
(indeed loops are abundant in random networks) and if the initial conditions
are sufficiently random. In the oscillating state, signals propagate in a
single direction and one or a few network loops are selected as driving loops
in which the excitation circulates periodically. We analyze the mechanism,
describe the oscillating states, identify the pacemaker loops and explain key
features of their distribution. This mechanism may play a role in epileptic
seizures.Comment: 5 pages, 4 figures included, submitted to Phys. Rev. Let
Period-Doubling Bifurcation in an Array of Coupled Stochastically Excitable Elements Subjected to Global Periodic Forcing
The collective behaviors of coupled, stochastically excitable elements subjected to global periodic forcing are investigated numerically and analytically. We show that the whole system undergoes a period-doubling bifurcation as the driving period decreases, while the individual elements still exhibit random excitations. Using a mean-field representation, we show that this macroscopic bifurcation behavior is caused by interactions between the random excitation, the refractory period, and recruitment (spatial cooperativity) of the excitable elements
Period-doubling Bifurcation in an Array of Coupled Stochastically-excitable Elements Subjected to Global Periodic Forcing
The collective behaviors of coupled, stochastically-excitable elements subjected to global periodic forcing are investigated numerically and analytically. We show that the whole system undergoes a period-doubling bifurcation as the driving period decreases, while the individual elements still exhibit random excitations. Using a mean-field representation, we show that this macroscopic bifurcation behavior is caused by interactions between the random excitation, the refractory period, and recruitment (spatial cooperativity) of the excitable elements
Effect of small-world topology on wave propagation on networks of excitable elements
We study excitation waves on a Newman-Watts small-world network model of
coupled excitable elements. Depending on the global coupling strength, we find
differing resilience to the added long-range links and different mechanisms of
propagation failure. For high coupling strengths, we show agreement between the
network and a reaction-diffusion model with additional mean-field term.
Employing this approximation, we are able to estimate the critical density of
long-range links for propagation failure.Comment: 19 pages, 8 figures and 5 pages supplementary materia
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