805 research outputs found
Stripe-hexagon competition in forced pattern forming systems with broken up-down symmetry
We investigate the response of two-dimensional pattern forming systems with a
broken up-down symmetry, such as chemical reactions, to spatially resonant
forcing and propose related experiments. The nonlinear behavior immediately
above threshold is analyzed in terms of amplitude equations suggested for a
and ratio between the wavelength of the spatial periodic forcing
and the wavelength of the pattern of the respective system. Both sets of
coupled amplitude equations are derived by a perturbative method from the
Lengyel-Epstein model describing a chemical reaction showing Turing patterns,
which gives us the opportunity to relate the generic response scenarios to a
specific pattern forming system. The nonlinear competition between stripe
patterns and distorted hexagons is explored and their range of existence,
stability and coexistence is determined. Whereas without modulations hexagonal
patterns are always preferred near onset of pattern formation, single mode
solutions (stripes) are favored close to threshold for modulation amplitudes
beyond some critical value. Hence distorted hexagons only occur in a finite
range of the control parameter and their interval of existence shrinks to zero
with increasing values of the modulation amplitude. Furthermore depending on
the modulation amplitude the transition between stripes and distorted hexagons
is either sub- or supercritical.Comment: 10 pages, 12 figures, submitted to Physical Review
Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction
The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results
Differential susceptibility to noise of mixed Turing and Hopf modes in a photosensitive chemical medium
We report on experiments with the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) when forced with a random (spatiotemporally) distributed illumination. Acting on a mixed mode consisting of oscillating spots, close enough to the Hopf and Turing codimension-two bifurcation, we observe attenuation of oscillations while the spatial pattern is preserved. Numerical simulations confirm and extend these results. All together these observations point out to a larger vulnerability of the Hopf with respect to the Turing mode when facing noise of intermediate intensity and small correlation parameters.Peer ReviewedPostprint (published version
Instabilities and Patterns in Coupled Reaction-Diffusion Layers
We study instabilities and pattern formation in reaction-diffusion layers
that are diffusively coupled. For two-layer systems of identical two-component
reactions, we analyze the stability of homogeneous steady states by exploiting
the block symmetric structure of the linear problem. There are eight possible
primary bifurcation scenarios, including a Turing-Turing bifurcation that
involves two disparate length scales whose ratio may be tuned via the
inter-layer coupling. For systems of -component layers and non-identical
layers, the linear problem's block form allows approximate decomposition into
lower-dimensional linear problems if the coupling is sufficiently weak. As an
example, we apply these results to a two-layer Brusselator system. The
competing length scales engineered within the linear problem are readily
apparent in numerical simulations of the full system. Selecting a :1
length scale ratio produces an unusual steady square pattern.Comment: 13 pages, 5 figures, accepted for publication in Phys. Rev.
Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system
The Lengyel-Epstein reaction-diffusion system of the CIMA reaction is revisited. We construct a Lyapunov function to show that the constant equilibrium solution is globally asymptotically stable when the feeding rate of iodide is small. We also show that for small spatial domains, all solutions eventually converge to a spatially homogeneous and time-periodic solution. (C) 2008 Elsevier Ltd. All rights reserved
Synchronization and oscillator death in oscillatory media with stirring
The effect of stirring in an inhomogeneous oscillatory medium is
investigated. We show that the stirring rate can control the macroscopic
behavior of the system producing collective oscillations (synchronization) or
complete quenching of the oscillations (oscillator death). We interpret the
homogenization rate due to mixing as a measure of global coupling and compare
the phase diagrams of stirred oscillatory media and of populations of globally
coupled oscillators.Comment: to appear in Phys. Rev. Let
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