22 research outputs found
Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
In this paper we study the effect of external harmonic forcing on a
one-dimensional oscillatory system described by the complex Ginzburg-Landau
equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous
state with no spatial structure is observed. The state becomes unstable to a
spatially periodic ``stripe'' state via a supercritical bifurcation as the
forcing amplitude decreases. An approximate phase equation is derived, and an
analytic solution for the stripe state is obtained, through which the
asymmetric behavior of the stability border of the state is explained. The
phase equation, in particular the analytic solution, is found to be very useful
in understanding the stability borders of the homogeneous and stripe states of
the forced CGLE.Comment: 6 pages, 4 figures, 2 column revtex format, to be published in Phys.
Rev.
Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model
Spatio-temporal bifurcations and complex dynamics in globally coupled
intrinsically bistable electrochemical systems with an S-shaped current-voltage
characteristic under galvanostatic control are studied theoretically on a
one-dimensional domain. The results are compared with the dynamics and the
bifurcation scenarios occurring in a closely related model which describes
pattern formation in semiconductors. Under galvanostatic control both systems
are unstable with respect to the formation of stationary large amplitude
current domains. The current domains as well as the homogeneous steady state
exhibit oscillatory instabilities for slow dynamics of the potential drop
across the double layer, or across the semiconductor device, respectively. The
interplay of the different instabilities leads to complex spatio-temporal
behavior. We find breathing current domains and chaotic spatio-temporal
dynamics in the electrochemical system. Comparing these findings with the
results obtained earlier for the semiconductor system, we outline bifurcation
scenarios leading to complex dynamics in globally coupled bistable systems with
subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE
http://pre.aps.or
Tunable diffusive lateral inhibition in chemical cells
The Belousov-Zhabotinsky (BZ) reaction has become the prototype of nonlinear chemical dynamics. Microfluidic techniques provide a convenient method for emulsifying BZ solutions into monodispersed drops with diameters of tens to hundreds of microns, providing a unique system in which reaction-diffusion theory can be quantitatively tested. In this work, we investigate monolayers of microfluidically generated BZ drops confined in close-packed two-dimensional (2D) arrays through experiments and finite element simulations. We describe the transition from oscillatory to stationary chemical states with increasing coupling strength, controlled by independently varying the reaction chemistry within a drop and diffusive flux between drops. For stationary drops, we studied how the ratio of stationary oxidized to stationary reduced drops varies with coupling strength. In addition, using simulation, we quantified the chemical heterogeneity sufficient to induce mixed stationary and oscillatory patterns