1,160 research outputs found
Spiral wave drift in an electric field and scroll wave instabilities
I present the numerical computation of speed and direction of the drift of a
spiral wave in an excitable medium in the presence of an electric field. In
contrast to earlier results, the drift speed presents a strong variation close
to the parameter value where the drift speed component along the field changes
direction. Using a simple phenomenological model and results from a numerical
linear stability analysis of scroll waves, I show this behavior can be
attributed to a resonance of the meander modes with the translation modes of
the spiral wave. Extending this phenomenological model to scroll waves also
clarifies the link between the drift and long wavelength instabilities of
scroll waves.Comment: Phys Rev E accepte
On propagation failure in 1 and 2 dimensional excitable media
We present a non-perturbative technique to study pulse dynamics in excitable
media. The method is used to study propagation failure in one-dimensional and
two-dimensional excitable media. In one-dimensional media we describe the
behaviour of pulses and wave trains near the saddle node bifurcation, where
propagation fails. The generalization of our method to two dimensions captures
the point where a broken front (or finger) starts to retract. We obtain
approximate expressions for the pulse shape, pulse velocity and scaling
behavior. The results are compared with numerical simulations and show good
agreement.Comment: accepted for publication in Chao
Phase Synchronization and Polarization Ordering of Globally-Coupled Oscillators
We introduce a prototype model for globally-coupled oscillators in which each
element is given an oscillation frequency and a preferential oscillation
direction (polarization), both randomly distributed. We found two collective
transitions: to phase synchronization and to polarization ordering. Introducing
a global-phase and a polarization order parameters, we show that the transition
to global-phase synchrony is found when the coupling overcomes a critical value
and that polarization order enhancement can not take place before global-phase
synchrony. We develop a self-consistent theory to determine both order
parameters in good agreement with numerical results
Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability
We analyze the way topological constraints and inhomogeneity in the
excitability influence the dynamics of spiral waves on spheres and punctured
spheres of excitable media. We generalize the definition of an index such that
it characterizes not only each spiral but also each hole in punctured,
oriented, compact, two-dimensional differentiable manifolds and show that the
sum of the indices is conserved and zero. We also show that heterogeneity and
geometry are responsible for the formation of various spiral wave attractors,
in particular, pairs of spirals in which one spiral acts as a source and a
second as a sink -- the latter similar to an antispiral. The results provide a
basis for the analysis of the propagation of waves in heterogeneous excitable
media in physical and biological systems.Comment: 5 pages, 6 Figures, major revisions, accepted for publication in
Phys. Rev.
Dynamical mechanism of atrial fibrillation: a topological approach
While spiral wave breakup has been implicated in the emergence of atrial
fibrillation, its role in maintaining this complex type of cardiac arrhythmia
is less clear. We used the Karma model of cardiac excitation to investigate the
dynamical mechanisms that sustain atrial fibrillation once it has been
established. The results of our numerical study show that spatiotemporally
chaotic dynamics in this regime can be described as a dynamical equilibrium
between topologically distinct types of transitions that increase or decrease
the number of wavelets, in general agreement with the multiple wavelets
hypothesis. Surprisingly, we found that the process of continuous excitation
waves breaking up into discontinuous pieces plays no role whatsoever in
maintaining spatiotemporal complexity. Instead this complexity is maintained as
a dynamical balance between wave coalescence -- a unique, previously
unidentified, topological process that increases the number of wavelets -- and
wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure
Delay Induced Excitability
We analyse the stochastic dynamics of a bistable system under the influence
of time-delayed feedback. Assuming an asymmetric potential, we show the
existence of a regime in which the systems dynamic displays excitability by
calculating the relevant residence time distributions and correlation times.
Experimentally we then observe this behaviour in the polarization dynamics of a
vertical cavity surface emitting laser with opto-electronic feedback. Extending
these observations to two-dimensional systems with dispersive coupling we
finally show numerically that delay induced excitability can lead to the
appearance of propagating wave-fronts and spirals.Comment: 5 pages, 6 figure
A normal form for excitable media
We present a normal form for travelling waves in one-dimensional excitable
media in form of a differential delay equation. The normal form is built around
the well-known saddle-node bifurcation generically present in excitable media.
Finite wavelength effects are captured by a delay. The normal form describes
the behaviour of single pulses in a periodic domain and also the richer
behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf
bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point,
and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We
verify the existence of these bifurcations in numerical simulations. The
parameters of the normal form are determined and its predictions are tested
against numerical simulations of partial differential equation models of
excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao
Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems
We study the dynamics of scroll vortices in excitable reaction-diffusion
systems analytically and numerically. We demonstrate that intrinsic
three-dimensional instability of a straight scroll leads to the formation of
helicoidal structures. This behavior originates from the competition between
the scroll curvature and unstable core dynamics. We show that the obtained
instability persists even beyond the meander core instability of
two-dimensional spiral wave.Comment: 4 pages, 5 figures, revte
Dynamical clustering in oscillator ensembles with time-dependent interactions
We consider an ensemble of coupled oscillators whose individual states, in
addition to the phase, are characterized by an internal variable with
autonomous evolution. The time scale of this evolution is different for each
oscillator, so that the ensemble is inhomogeneous with respect to the internal
variable. Interactions between oscillators depend on this variable and thus
vary with time. We show that as the inhomogeneity of time scales in the
internal evolution grows, the system undergoes a critical transition between
ordered and incoherent states. This transition is mediated by a regime of
dynamical clustering, where the ensemble recurrently splits into groups formed
by varying subpopulations.Comment: 4 pages, 3 figure
Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators
We show that a wide class of uncoupled limit cycle oscillators can be
in-phase synchronized by common weak additive noise. An expression of the
Lyapunov exponent is analytically derived to study the stability of the
noise-driven synchronizing state. The result shows that such a synchronization
can be achieved in a broad class of oscillators with little constraint on their
intrinsic property. On the other hand, the leaky integrate-and-fire neuron
oscillators do not belong to this class, generating intermittent phase slips
according to a power low distribution of their intervals.Comment: 10 pages, 3 figure
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