259 research outputs found
Front and Turing patterns induced by Mexican-hat-like nonlocal feedback
We consider the effects of a Mexican-hat-shaped nonlocal spatial coupling,
i.e., symmetric long-range inhibition superimposed with short-range excitation,
upon front propagation in a model of a bistable reaction-diffusion system. We
show that the velocity of front propagation can be controlled up to a certain
coupling strength beyond which spatially periodic patterns, such as Turing
patterns or coexistence of spatially homogeneous solutions and Turing patterns,
may be induced. This behaviour is investigated through a linear stability
analysis of the spatially homogeneous steady states and numerical
investigations of the full nonlinear equations in dependence upon the nonlocal
coupling strength and the ratio of the excitatory and inhibitory coupling
ranges.Comment: Accepted in EP
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
Nonlocal control of pulse propagation in excitable media
We study the effects of nonlocal control of pulse propagation in excitable
media. As a generic example for an excitable medium the FitzHugh-Nagumo model
with diffusion in the activator variable is considered. Nonlocal coupling in
form of an integral term with a spatial kernel is added. We find that the
nonlocal coupling modifies the propagating pulses of the reaction-diffusion
system such that a variety of spatio-temporal patterns are generated including
acceleration, deceleration, suppression, or generation of pulses, multiple
pulses, and blinking pulse trains. It is shown that one can observe these
effects for various choices of the integral kernel and the coupling scheme,
provided that the control strength and spatial extension of the integral kernel
is appropriate. In addition, an analytical procedure is developed to describe
the stability borders of the spatially homogeneous steady state in control
parameter space in dependence on the parameters of the nonlocal coupling
Amplitude chimeras and chimera death in dynamical networks
We find chimera states with respect to amplitude dynamics in a network of
Stuart-Landau oscillators. These partially coherent and partially incoherent
spatio-temporal patterns appear due to the interplay of nonlocal network
topology and symmetry-breaking coupling. As the coupling range is increased,
the oscillations are quenched, amplitude chimeras disappear and the network
enters a symmetry-breaking stationary state. This particular regime is a novel
pattern which we call chimera death. It is characterized by the coexistence of
spatially coherent and incoherent inhomogeneous steady states and therefore
combines the features of chimera state and oscillation death. Additionally, we
show two different transition scenarios from amplitude chimera to chimera
death. Moreover, for amplitude chimeras we uncover the mechanism of transition
towards in-phase synchronized regime and discuss the role of initial
conditions
Synchronization of organ pipes
We investigate synchronization of coupled organ pipes. Synchronization and
reflection in the organ lead to undesired weakening of the sound in special
cases. Recent experiments have shown that sound interaction is highly complex
and nonlinear, however, we show that two delay-coupled Van-der-Pol oscillators
appear to be a good model for the occurring dynamical phenomena. Here the
coupling is realized as distance-dependent, or time-delayed, equivalently.
Analytically, we investigate the synchronization frequency and bifurcation
scenarios which occur at the boundaries of the Arnold tongues. We successfully
compare our results to experimental data
Delay-induced patterns in a two-dimensional lattice of coupled oscillators
We show how a variety of stable spatio-temporal periodic patterns can be
created in 2D-lattices of coupled oscillators with non-homogeneous coupling
delays. A "hybrid dispersion relation" is introduced, which allows studying the
stability of time-periodic patterns analytically in the limit of large delay.
The results are illustrated using the FitzHugh-Nagumo coupled neurons as well
as coupled limit cycle (Stuart-Landau) oscillators
- …