Photosensitive Belousov-Zhabotinsky Reaction Research Articles

Density wave propagation of a wave train in a closed excitable medium

A wave train in an excitable reaction-diffusion medium shows a variety of spatiotemporal patterns as a result of interactions between the individual waves. In this paper, we report a novel spatiotemporal pattern in a wave train in a closed excitable medium. We carried out experiments using a photosensitive Belousov-Zhabotinsky reaction with Ru(bpy)(3)(2+) as a catalyst and a numerical calculation using the FitzHugh-Nagumo equation. A wave train was locally distributed as an initial condition and the number of waves was systematically varied. In both the experiment and numerical calculation, density wave propagation was formed in a wave train during relaxation with a large number of waves. Our results suggest that density wave propagation originates from inhibitory interaction between the waves.

Photoexcited Chemical Wave in the Ruthenium-Catalyzed Belousov–Zhabotinsky Reaction

The excitation of the photosensitive Belousov-Zhabotinsky (BZ) reaction induced by light stimulation was systematically investigated. A stepwise increase in the light intensity induced the excitation, whereas a stepwise decrease did not induce the excitation. The threshold values for the excitation were found to be a function of the initial and final light intensities, time variation in light intensity, and the concentration of NaBrO(3). The experimental results were qualitatively reproduced by a theoretical calculation based on a three-variable Oregonator model modified for the photosensitive BZ reaction. These results suggest that although the steady light irradiation is known to inhibit oscillation and chemical waves in the BZ system under almost all conditions, the stepwise increase in the light irradiation leads to the rapid production of an activator, resulting in the photoexcitation.

Phase Wave between Two Oscillators in the Photosensitive Belousov−Zhabotinsky Reaction Depending on the Difference in the Illumination Time

To investigate the nature of the phase wave between two connected oscillators, the photosensitive Belousov-Zhabotinsky (BZ) reaction was examined for two connected circular reaction fields, which were drawn by using computer software and then projected on a filter paper soaked with BZ solution by using a liquid-crystal projector. The difference in the time at which illumination was terminated between the two circles (Deltat(0)) was changed to control the time at which the phase wave was induced. When Deltat(0) was small (0-3 s), the phase wave normally propagated on the two circles in one direction. In contrast, when Deltat(0) was large (6-10 s), the velocity of the wave decreased near the intersection of the two circles. These different features are discussed in relation to the excitability of the circles and Deltat(0). The experimental results were qualitatively reproduced by a numerical calculation based on the modified three-variable Oregonator model that included photosensitivity.

Oscillation in Penetration Distance in a Train of Chemical Pulses Propagating in an Optically Constrained Narrowing Channel

A chemical wave train propagating in a narrowing excitable channel surrounded by a nonexcitable field is investigated by using a photosensitive Belousov-Zhabotinsky (BZ) reaction. The considered geometry is created as a dark triangle surrounded by an illuminated area where the reaction is suppressed by the light-induced generation of bromide ion. For a low illumination level, a pulse train terminates at a constant position. However, as the light intensity increases, the position at which subsequent pulses disappear changes periodically, so that the period-doubling of penetration depth occurs. Two-dimensional simulations based on a modified Oregonator model for the photosensitive BZ reaction reproduce the essential features of the experimental observation.

Wave Propagation in the Photosensitive Belousov−Zhabotinsky Reaction Across an Asymmetric Gap

The photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated at an asymmetrically illuminated gap, which was drawn using computer software and then projected on a filter paper soaked with BZ solution using a liquid-crystal projector. The probability of the chemical wave passing through the gap with asymmetric illumination was different from that through its mirror image. The location at which the wave disappeared and the time delay of the chemical wave passing through the gap changed depending on the velocity of chemical wave propagation. The experimental results were qualitatively reproduced by a theoretical calculation based on the three-variable Oregonator model that included photosensitivity. These results suggest that the photosensitive BZ reaction may be useful for studying spatiotemporal development that depends on the geometry of excitable fields.

Experimental validation of binary collisions between wave fragments in the photosensitive Belousov–Zhabotinsky reaction

We present experimental verification of wave fragment collisions in the sub-excitable Belousov–Zhabotinsky medium observed previously in simulation [Adamatzky A, De Lacy Costello B. Binary collisions between wave fragments in a sub-excitable Belousov–Zhabotinsky medium. Chaos, Solitons & Fractals 2007;34:307–15]. We have reproduced in chemical experiments the majority of the collisions observed in simulation including annihilation, fusion and quasi-elastic types. The method we present is capable of implementing information transfer without any rigidly controlled architecture – fragments are simply introduced into an “arena” which consists of a large area of gel illuminated with a uniform light level – controlled at a level close to the sub-excitable threshold. Therefore, the fragments of excitation both pre and post collision possess a considerable freedom of movement when compared to previous implementations of information transfer in chemical systems. This chemical verification of previous theoretical results brings closer the possibility of utilising this phenomenon for implementing collision-based gates, signal tuning and programming of collision-based computers based upon excitable chemical reactions.

Collective behavior of stabilized reaction-diffusion waves

Stabilized wave segments in the photosensitive Belousov-Zhabotinsky reaction are directionally controlled with intensity gradients in the applied illumination. The constant-velocity waves behave like self-propelled particles, and multiple waves interact via an applied interaction potential. Alignment arises from the intrinsic properties of the interacting waves, leading to processional and rotational behavior.

Survival versus collapse: Abrupt drop of excitability kills the traveling pulse, while gradual change results in adaptation

Excitable media show changes in their basic characteristics that reflect temporal changes in the environment. In the photosensitive Belousov-Zhabotinsky (BZ) reaction, excitability is decreased by illumination. We found that a traveling pulse failed to propagate when a certain level of light intensity was switched on abruptly, but the pulse continued propagating when the light intensity reached the same level gradually. We investigated the mechanism of adaptation of pulse propagation to the change in light intensity using two mathematical models, the Oregonator model (a specific model for the photosensitive BZ reaction), and the FitzHugh-Nagumo model (a generic model for excitable media). The appearance of a characteristic such as adaptation is shown to be a general feature for a traveling pulse in excitable media.

Characteristic Features in the Collision of Chemical Waves Depending on the Aspect Ratio of a Rectangular Field

The photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated on a double rectangular field composed of two rectangular routes, which was drawn using computer software and then projected using a liquid-crystal projector on a filter paper soaked with BZ solution. When two chemical waves were generated on the rectangular routes as the initial condition, the nature of the collision of the waves could be theoretically classified into four categories depending on the initial phase difference between the two waves and the aspect ratio of the rectangular routes. The experimental results were consistent with the features of the theoretical prediction. These results suggest that the feature of wave propagation characteristically develops depending on the geometry of the excitable fields.

Coexistence of Wave Propagation and Oscillation in the Photosensitive Belousov−Zhabotinsky Reaction on a Circular Route

The photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated on a circular ring, which was drawn using computer software and then projected on a film soaked with BZ solution using a liquid-crystal projector. Under the initial conditions, a chemical wave propagated with a constant velocity on the black ring under a bright background. When the background was rapidly changed to dark, coexistence of the oscillation on part of the ring and propagation of the chemical wave on the other part was observed. These experimental results are discussed in relation to the nature of the photosensitive BZ reaction and theoretically reproduced based on a reaction-diffusion system using the modified Oregonator model.

Kinematic description of wave propagation through a chemical diode

The geometry of an active medium can cause wave blocking and induce unidirectional propagation. This well established phenomenon was studied in a previous paper within the framework of the photosensitive Belousov-Zhabotinsky reaction and the associated Oregonator model. In the present paper, as an extension of that study, the main factors that influence this phenomenon are interpreted in terms of a kinematic model.

Creating bound states in excitable media by means of nonlocal coupling

We consider pulses of excitation in reaction-diffusion systems subjected to nonlocal coupling. This coupling represents long-range connections between the elements of the medium; the connection strength decays exponentially with the distance. Without coupling, pulses interact only repulsively and bound states with two or more pulses propagating at the same velocity are impossible. Upon switching on nonlocal coupling, pulses begin to interact attractively and form bound states. First we present numerical results on the emergence of bound states in the excitable Oregonator model for the photosensitive Belousov-Zhabotinsky reaction with nonlocal coupling. Then we show that the appearance of bound states is provided solely by the exponential decay of nonlocal coupling and thus can be found in a wide class of excitable systems, regardless of the particular kinetics. The theoretical explanation of the emergence of bound states is based on the bifurcation analysis of the profile equations that describe the spatial shape of pulses. The central object is a codimension-4 homoclinic orbit which exists for zero coupling strength. The emergence of bound states is described by the bifurcation to 2-homoclinic solutions from the codimension-4 homoclinic orbit upon switching on nonlocal coupling. We stress that the high codimension of the bifurcation to bound states is generic, provided that the coupling range is sufficiently large.

Spatiotemporal dynamics of networks of excitable nodes

A network of excitable nodes based on the photosensitive Belousov-Zhabotinsky reaction is studied in experiments and simulations. The addressable medium allows both local and nonlocal links between the nodes. The initial spread of excitation across the network as well as the asymptotic oscillatory behavior are described. Synchronization of the spatiotemporal dynamics occurs by entrainment to high-frequency network pacemakers formed by excitation loops. Analysis of the asymptotic behavior reveals that the dynamics of the network is governed by a subnetwork selected during the initial transient period.

Interactive Propagation of Photosensitive Chemical Waves on Two Circular Routes

The propagation of chemical waves in the photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated using an excitable field composed of two rings in slight contact, which were drawn using computer software and then projected on a film soaked with BZ solution using a liquid-crystal projector. When the initial phase difference between the two chemical waves in the individual rings was smaller than a critical value, this initial value was maintained after collision of the chemical waves. However, when the initial phase difference was larger than this critical value, the phase difference converged to the same value after the second collision. The critical value increased with an increase in the thickness of the rings. These experimental results on the geometry of the excitable field are discussed in relation to the nature of chemical wave propagation. These results suggest that the photosensitive BZ reaction may be useful for creating spatiotemporal patterns that depend on the geometric arrangement of excitable fields.

Controlling the Ru-catalyzed Belousov–Zhabotinsky reaction by addition of hydroquinone

Oscillation patterns in the photosensitive Belousov–Zhabotinsky reaction composed of malonic acid / BrO 3 - / Ru ( bpy ) 3 2 + / H + were modulated by addition of less than 100 mM of hydroquinone. In dark, the limit cycle oscillations bifurcated into mixed-mode oscillations of 1 1 and 1 2 with hydroquinone concentration, where the superscripts indicate the number of small-amplitude oscillations. Under illumination, three types of pattern change were observed depending on the initial composition of the reaction mixture. A probable mechanism to explain the role of hydroquinone is proposed on the basis of the Field–Körös–Noyes mechanism and the photocycle of the Ru-catalyst.

Dynamics of rigidly rotating spirals under periodic modulation of excitability

The dynamics of rigidly rotating spiral waves under periodic modulation of excitability is studied experimentally in the photosensitive Belousov–Zhabotinsky reaction. The experiments of sinusoidal and pulsatory modulation reveal that the motion of the spiral tips can be forced to describe a wide range of cycloidal trajectories, depending strongly on the modulation period. The results are complemented with numerical simulations and discussed in the framework of the kinematical theory. We found that the critical parameter for a linear resonance drift under the periodic modulation is not only ‘the modulation period’, as reported earlier, but also the amplitude and duration of modulation.

Bloch-front turbulence: theory and experiments

We report on experimental and theoretical findings of front destabilization that causes spontaneous spiral–vortex nucleation and produces a state of spatio-temporal disorder. The experiments were carried out on an oscillatory photosensitive Belousov–Zhabotinsky reaction that is periodically forced in time. Numerical studies were carried out on a modified Complex Ginzburg–Landau equation and on the FitzHugh–Nagumo model. Using velocity–curvature relations for fronts we associate the onset of spatio-temporal disorder with the Nonequilibrium Ising Bloch (NIB) bifurcation, and study the generic patterns that form on both sides of the bifurcation as the distance from it is increased.

Propagation of Photosensitive Chemical Waves on the Circular Routes

The propagation of chemical waves in the photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated using an excitable field in the shape of a circular ring or figure "8" that was drawn by computer software and then projected on a film soaked with BZ solution using a liquid-crystal projector. For a chemical wave in a circular reaction field, the shape of the chemical wave was investigated depending on the ratio of the inner and outer radii. When two chemical waves were generated on a field shaped like a figure "8" (one chemical wave in each circle) as the initial condition, the location of the collision of the waves either was constant or alternated depending on the degree of overlap of the two circular rings. These experimental results were analyzed on the basis of a geometrical discussion and theoretically reproduced on the basis of a reaction-diffusion system using a modified Oregonator model. These results suggest that the photosensitive BZ reaction may be useful for creating spatio-temporal patterns depending on the geometric arrangement of excitable fields.

Forced excitations and excitable chaos in the photosensitive Oregonator under periodic sinusoidal perturbations

The responses of an excitable system to external periodic perturbations are studied by using the photosensitive Oregonator that is a three variable model of the photosensitive Belousov–Zhabotinsky reaction. The system is set at the vicinity of the subcritical Hopf bifurcation point, and sinusoidal perturbation is given by light: ϕ ( α , ν ) = ϕ 0 − α A 0 sin ⁡ ( 2 π ν τ ) . The dynamic threshold for firing appears as a U-shaped line in ν – α plane. Under high-frequency perturbations, the system shows a subthreshold period-doubling cascade, subthreshold chaotic responses (excitable chaos) and reaches firing chaos as a result of expansion of orbits around the fixed point.

Different operations on a single circuit: Field computation on an excitable chemical system

Recently, it has been proposed that various kinds of time operations can be performed using an excitable field, mainly based on computer simulation. In this study, we performed experiments toward the realization of a time operation, such as time-difference detection. We used the photosensitive Belousov–Zhabotinsky reaction as a spatially distributed excitable field. We found that a single geometrical circuit can perform different operations with changes in the intensity of light illumination. The experimental results are discussed in relation to the idea of a non-Neumann-type computational device.