Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction

Front interaction induces excitable behavior

Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an alternative mechanism based on the coexistence of two homogeneous stable states and spatial coupling. We show the existence of a threshold for perturbations of the homogeneous state. Subthreshold perturbations decay exponentially. Superthreshold perturbations induce the emergence of a long-lived structure formed by two back to back fronts that join the two homogeneous states. While in typical excitability the trajectory follows the remnants of a limit cycle, here reinjection is provided by front interaction, such that fronts slowly approach each other until eventually annihilating. This front-mediated mechanism shows that extended systems with no oscillatory regimes can display excitability.

Complex spatiotemporal behavior in the photosensitive ferroin-bromate-4-nitrophenol reaction

Investigation illustrates that the bromate-4-nitrophenol reaction in a stirred batch reactor undergoes spontaneous oscillations under very broad initial reactant concentrations. The addition of ferroin has subtle influences on the nonlinear behavior, in which the frequency and total number of oscillations were greatly reduced at a low or high ferroin concentration, as opposed to the significant increase at a moderate ferroin concentration. Temporal oscillations with a modulating frequency were also observed in the ferroin-bromate-4-nitrophenol system. In a capillary tube the ferroin-bromate-4-nitrophenol reaction generated propagating wave trains with various complex behaviors such as period-doubled intermittent propagation failure. Illumination was found to have a profound effect on the temporal oscillations in the bromate-4-nitrophenol reaction and on those long lasting wave activities. Spectroscopic studies were able to identify 1,4-benzoquinone, 2-bromo-1,4-benzoquinone, and 2-bromo-4-nitrophenol as major components during the reaction.

Theory for the spatiotemporal dynamics of domain walls close to a nonequilibrium Ising-Bloch transition

We derive a generic model for the interaction of domain walls close to a nonequilibrium-Bloch transition. The universal scenario predicted by the model includes stationary Ising and Bloch localized structures (dissipative solitons), as well as drifting and oscillating Bloch structures. Our theory also explains the behavior of Bloch walls during a collision. The results are confirmed by numerical simulations of the Ginzburg-Landau equation forced at twice its natural frequency and are in agreement with previous observations in several physical systems.

Pattern formation controlled by time-delayed feedback in bistable media

Effects of time-delayed feedback on pattern formation are studied both numerically and theoretically in a bistable reaction-diffusion model. The time-delayed feedback applied to the activator and/or the inhibitor alters the behavior of the nonequilibrium Ising-Bloch (NIB) bifurcation. If the intensities of the feedbacks applied to the two species are identical, only the velocities of Bloch fronts are changed. If the intensities are different, both the critical point of the NIB bifurcation and the threshold of stability of front to transverse perturbations are changed. The effect of time-delayed feedback on the activator opposes the effect of time-delayed feedback on the inhibitor. When the time-delayed feedback is applied individually to one of the species, positive and negative feedbacks make the bifurcation point shift to different directions. The time-delayed feedback provides a flexible way to control the NIB bifurcation and the pattern formation.

Experimentally observed route to spatiotemporal chaos in an extended one-dimensional array of convective oscillators

We report experimental evidence of the route to spatiotemporal chaos in a large one-dimensional array of hotspots in a thermoconvective system. As the driving force is increased, a stationary cellular pattern becomes unstable toward a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveal the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of high spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling than the previous mixed pattern and enables us to find out that this beating phenomenon is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phaselike synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.

Two-dimensional front dynamics and spatial solitons in a nonlinear optical system

Two-dimensional fronts and coarsening dynamics with a t{1/2} power law are analyzed experimentally and theoretically in a nonlinear optical system of a sodium vapor cell with single-mirror feedback. Modifications of the t{1/2} power law are observed in the vicinity of a modulational instability leading to the formation of spatial solitons of different sizes. The experimental and numerical observations give direct evidence for the locking of fronts as the mechanism of soliton formation. A phenomenological equation for the dynamics of the domain radius explains the observed behavior.

Reciprocal oscillons and nonmonotonic fronts in forced nonequilibrium systems

The formation of oscillons in a synchronously oscillating background is studied in the context of both damped and self-exciting oscillatory media. Using the forced complex Ginzburg-Landau equation we show that such states bifurcate from finite amplitude homogenous states near the 2:1 resonance boundary. In each case we identify a region in parameter space containing a finite multiplicity of coexisting stable oscillons with different structure. Stable time-periodic monotonic and nonmonotonic frontlike states are present in an overlapping region. Both types of structure are related to the presence of a Maxwell point between the zero and finite amplitude homogeneous states.

Resonant and nonresonant patterns in forced oscillators

Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.

Effect of inhomogeneities on spiral wave dynamics in the Belousov-Zhabotinsky reaction

We examine the effects of controlled, slowly varying spatial inhomogeneities on spiral wave dynamics in the light sensitive Belousov-Zhabotinsky chemical reaction-diffusion system. We measure the speed of the grain boundary that separates two spirals, the speed of the lower frequency spiral being swept away by the grain boundary, and the speed of the slow drift of the highest frequency spiral. The grain boundary speeds are shown to be related to the frequency of rotation and wave number of the spiral pattern, as predicted from analysis of the complex Ginzburg-Landau equation [M. Hendrey, Phys. Rev. Lett.10.1103/PhysRevLett.82.859 82, 859 (1999); M. Hendrey,, Phys. Rev. E10.1103/PhysRevE.61.4943 61, 4943 (2000)].

Out-of-phase oscillatory Turing patterns in a bistable reaction-diffusion system

A new type of out-of-phase oscillatory Turing pattern is found in simulations of a simple two-variable model of a bistable reaction-diffusion system consisting of an autocatalytic activator reacting with a substrate that is replenished by a flow. This class of models can describe pH oscillators or enzymatic reactions. No Hopf instability is necessary for this type of oscillatory Turing pattern.