Light-sensitive Belousov-Zhabotinsky Research Articles

Light sensitive Belousov–Zhabotinsky medium accommodates multiple logic gates

Computational functionality has been implemented successfully on chemical reactions in living systems. In the case of Belousov–Zhabotinsky (BZ) reaction, this was achieved by using collision-based techniques and by exploiting the light sensitivity of BZ. In order to unveil the computational capacity of the light sensitive BZ medium and the possibility to implement re-configurable logic, the design of multiple logic gates in a fixed BZ reservoir was investigated. The three basic logic gates (namely NOT, OR and AND) were studied to prove the Turing completeness of the architecture. Namely, all possible Boolean functions can be implemented as a combination of these logic gates. Nonetheless, a more complicated logic function was investigated, aiming to illustrate further capabilities of a fixed size BZ reservoir. The experiments executed within this study were implemented with a Cellular Automata (CA)-based model of the Oregonator equations that simulate excitation and wave propagation on a light sensitive BZ thin film. Given that conventional or von Neumann architecture computations is proved possible on the proposed configuration, the next step would be the realization of unconventional types of computation, such as neuromorphic and fuzzy computations, where the chemical substrate may prove more efficient than silicon.

ON POLYMORPHIC LOGICAL GATES IN SUBEXCITABLE CHEMICAL MEDIUM

In a subexcitable light-sensitive Belousov–Zhabotinsky (BZ) chemical medium an asymmetric disturbance causes the formation of localized traveling wave-fragments. Under the right conditions these wave-fragments can conserve their shape and velocity vectors for extended time periods. The size and life span of a fragment depend on the illumination level of the medium. When two or more wave-fragments collide they annihilate or merge into a new wave-fragment. In computer simulations based on the Oregonator model, we demonstrate that the outcomes of inter-fragment collisions can be controlled by varying the illumination level applied to the medium. We interpret these wave-fragments as values of Boolean variables and design collision-based polymorphic logical gates. The gate implements operation XNOR for low illumination, and it acts as NOR gate for high illumination. As a NOR gate is a universal gate, then we are able to demonstrate that a simulated light sensitive BZ medium exhibits computational universality.

Spontaneous suppression of spiral turbulence based on feedback strategy

Control of defect-mediated turbulence or spiral turbulence has been a subject of pattern dynamics study in the last two decades. As a result, many control strategies has been proposed in theory and tested in computer simulation. Here we propose a self-regulation system that can spontaneously eliminate topological defects in the reaction-diffusion system that suffers from the Doppler instability. The core of the self-regulation scheme is a feedback introduction of local inhomogeneities around spiral tips. We used modified FitzHugh-Nagumo model in computer simulations and light-sensitive Belousov-Zhabotinsky reaction in experiments to test the functionality of the proposed system. We found that if the inhomogeneities were induced on the spiral tips once they were identified, the spiral can be exterminated thus the spiral turbulence can be controlled. Compared with the studies on anatomic obstacles in heart, this self-regulation model may provide a possible mechanism for spontaneous termination of cardiac fibrillation.

Intelligent image sensor based on probing the evolution of redox potentials distributed in reaction–diffusion medium

Belousov–Zhabotinsky (BZ) reaction–diffusion medium, considered as a continuously distributed information processing system operating in a highly parallel mode, can be used to process images. A sol–gel method is used to prepare the light-sensitive BZ reaction–diffusion medium, which forms on a circuit board containing 8 × 8 channel matrix platinum electrodes. This medium ensures both reaction running and potential detecting. BZ reaction is excited by projecting an image (input-image) on the light-sensitive BZ medium, followed by the chemical waves’ (output-image) occurrence in the BZ medium. The imaging process in BZ medium is an evolutional one, including image inversion and boundary-enhancement function. Redox potentials distributed in the BZ medium reflect the evolution of the output-image and are detected synchronizing with the image evolution process. The output-image is reconstructed in the form of the distribution of redox potentials. The light-sensitive BZ medium and the potential detecting equipment can be developed as an intelligent image sensor. This system enabled us to open a new way to construct image sensors.

Simple Collision-Based Chemical Logic Gates with Adaptive Computing

We present a method that is capable of implementing information transfer without any rigidly controlled architecture using the light-sensitive Belousov-Zhabotinsky (BZ) reaction system. Chemical wave fragments are injected into a subexcitable area and their collisions result in annihilation, fusion or quasi-elastic interactions depending on their initial positions. 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. We propose that the collision of such wave fragments can be controlled automatically through adaptive computing. By extension, forms of unconventional computing, i.e., massively parallel non-linear computers, can be realised by such an approach. In this study we present initial results from using a simple evolutionary algorithm to design Boolean logic gates within the BZ system.

Spiral formation and degeneration in heterogeneous excitable media

Spontaneous spiral formation occurs when an excitation wave is input to a heterogeneous network of low- and high-light-intensity cells projected onto a light-sensitive Belousov-Zhabotinsky reaction. The range of network conditions where spirals form is increased if two waves are input at critical time intervals. Spirals degenerate to form multiple spirals and spirals trapped within excitable cells. Spiral formation and degeneration is dependent on network excitability, cell size, and network size. Results exhibit parallels with spiral formation in excitable biological systems such as the heart.

Implementation of glider guns in the light-sensitive Belousov-Zhabotinsky medium

In cellular automata models a glider gun is an oscillating pattern of nonquiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical gates and thus realize universal computation. The glider gun is the only means of ensuring the negation operation without additional external input and therefore is an essential component of a collision-based computing circuit. We demonstrate the existence of glider-gun-like structures in both experimental and numerical studies of an excitable chemical system-the light-sensitive Belousov-Zhabotinsky reaction. These discoveries could provide the basis for future designs of collision-based reaction-diffusion computers.

Efficient control of spiral wave location in an excitable medium with localized heterogeneities

We show that a spiral wave core can be guided by feedback control through a two-dimensional (2D) medium along a virtual 1D detector of given shape. To this aim, short perturbations of excitability are applied globally to the medium each time the spiral wave front is tangent to the detector, or touches its open ends. This relatively simple and robust feedback algorithm is realized in experiments with the light-sensitive Belousov–Zhabotinsky (BZ) medium and in numerical simulations of the underlying Oregonator model. A theory is developed that reduces the description of the spiral wave drift to an iterated map from which the drift velocity field for the motion of the spiral core can be obtained. This drift velocity field predicts both the transient as well as the stationary trajectories of the drifting spiral waves in good agreement with experimental and numerical data. It is shown that the drift velocity is limited by instabilities which arise under high perturbation strength or large delay time. We propose a method to suppress the observed instabilities in order to increase the velocity of feedback mediated resonant drift. Our results might be useful for the control of spiral wave location in a wide variety of excitable media.

Coherence resonance in a chemical excitable system driven by coloured noise

We investigate how the temporal correlation in excitable systems driven by external noise affects the coherence of the system's response. The coupling to the fluctuating environment is introduced via fluctuations of a bifurcation parameter that controls the local dynamics of the light-sensitive Belousov-Zhabotinsky reaction and of its numerical description, the Oregonator model. Both systems are brought from a highly incoherent regime to a coherent one by an appropriate choice of the correlation time and keeping noise variance constant. This effect has been found both for an Ornstein-Uhlenbeck process and for a dichotomous telegraph signal. In the latter case, we are able to connect the optimal correlation time, for which the system behaviour is most coherent, with a characteristic time scale of the system.

Compensation of curvature effects by illumination

Front deformation of initially planar excitation waves can be observed in nonplanar media or in spatially heterogeneously illuminated systems. The deformation of propagating reaction–diffusion waves in either of these systems has been investigated earlier separately. Here we present a combination of both heterogeneous systems, which can lead to a compensation of wave deformations. Our theoretical analysis of the evolution of propagating excitation waves, based on the framework of a kinematical theory, shows that the curvature effect can be compensated by illumination. Supporting experiments were performed with the light-sensitive Belousov–Zhabotinsky system.

Period-Doubling of Spiral Waves and Defects

Motivated by experimental observations in the light-sensitive Belousov–Zhabotinsky reaction and subsequent numerical works, we discuss period-doubling bifurcations of spiral waves and other coherent structures. We report on explanations of the observed phenomena which involve a detailed analysis of spectra, and of the associated eigenfunctions, of defects on bounded and unbounded domains.

Spiral wave dynamics under feedback via an equilateral triangular sensory domain

We perform a numerical study of the trajectories of spiral wave cores in excitable systems whose excitability is modulated in proportion to the integral of the activity in a sensory domain in the shape of an equilateral triangle. As a result of this domain shape having vertices opposite sides, unusual forms of lobed limit cycles occur, which are destroyed and then re-form as the domain size is varied. Some key results are also demonstrated experimentally using the light-sensitive Belousov-Zhabotinsky reaction. To characterize the observed behavior, we introduce the concept of express and stagnation zones, which are regions where the trajectory moves particularly rapidly or slowly. The location and strength of the zones far from the domain are accounted for by approximating the parts of the spiral wave crossing the domain by a series of plane waves.

Successive splitting of autowaves in a nonlinear chemical reaction medium

The phenomenon of wave splitting is investigated in a two-dimensional excitable light-sensitive Belousov-Zhabotinsky reaction medium after extremely changing the intensity of illuminated light for a short time. It is found that successive wave splitting and nonannihilation collision between two waves of different amplitudes occur spontaneously under narrow experimental conditions. Experimental observations are approximately reproduced in the specific parameter range by a numerical simulation with a Bär-Eiswirth model.

Stabilization of unstable rigid rotation of spiral waves in excitable media

Depending on the parameters of two-dimensional excitable or oscillatory media rigidly rotating or meandering spiral waves are observed. The transition from rigid rotation to meandering motion occurs via a supercritical Hopf bifurcation. To stabilize rigid rotation in a parameter range beyond the Hopf bifurcation, we propose and successfully apply a proportional control algorithm as well as time delay autosynchronization. Both control methods are noninvasive. This allows for determination of the parameters of unstable rigid rotation of spiral waves either for a model or an experimental system. Using the Oregonator model for the light-sensitive Belousov-Zhabotinsky reaction as a representative example we show that quite naturally some latency time appears in the control loop, and propose an efficient method to overcome its destabilizing influence.

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.

Wave instability induced by nonlocal spatial coupling in a model of the light-sensitive Belousov-Zhabotinsky reaction

We study spatiotemporal patterns resulting from instabilities induced by nonlocal spatial coupling in the Oregonator model of the light-sensitive Belousov-Zhabotinsky reaction. In this system, nonlocal coupling can be externally imposed by means of an optical feedback loop which links the intensity of locally applied illumination with the activity in a certain vicinity of a particular point weighted by a given coupling function. This effect is included in the three-variable Oregonator model by an additional integral term in the photochemically induced bromide flow. A linear stability analysis of this modified Oregonator model predicts that wave and Turing instabilities of the homogeneous steady state can be induced for experimentally realistic parameter values. In particular, we find that a long-range inhibition in the optical feedback leads to a Turing instability, while a long-range activation induces wave patterns. Using a weakly nonlinear analysis, we derive amplitude equations for the wave instability which are valid close to the instability threshold. Therein, we find that the wave instability occurs supercritically or subcritically and that traveling waves are preferred over standing waves. The results of the theoretical analysis are in good agreement with numerical simulations of the model near the wave instability threshold. For larger distances from threshold, a secondary breathing instability is found for traveling waves.

COHERENCE RESONANCE PHENOMENA IN AN EXCITABLE SYSTEM DRIVEN BY COLORED NOISE

We study the coherence of noise-induced excitations in a modified stochastic Oregonator model for the light-sensitive Belousov-Zhabotinsky (BZ) reaction assuming that the intensity of the applied illumination is a spatio-temporal stochastic field with finite correlation time and correlation length. For a single excitable element, we find coherence resonance (CR) with respect to the correlation time. In the spatially extended medium of diffusively coupled excitable elements, we observe CR for suitable combinations of the correlation time and length of the noise.

Derivation of a quantitative minimal model from a detailed elementary-step mechanism supported by mathematical coupling analysis

Accurate experimental data increasingly allow the development of detailed elementary-step mechanisms for complex chemical and biochemical reaction systems. Model reduction techniques are widely applied to obtain representations in lower-dimensional phase space which are more suitable for mathematical analysis, efficient numerical simulation, and model-based control tasks. Here, we exploit a recently implemented numerical algorithm for error-controlled computation of the minimum dimension required for a still accurate reduced mechanism based on automatic time scale decomposition and relaxation of fast modes. We determine species contributions to the active (slow) dynamical modes of the reaction system and exploit this information in combination with quasi-steady-state and partial-equilibrium approximations for explicit model reduction of a novel detailed chemical mechanism for the Ru-catalyzed light-sensitive Belousov-Zhabotinsky reaction. The existence of a minimum dimension of seven is demonstrated to be mandatory for the reduced model to show good quantitative consistency with the full model in numerical simulations. We derive such a maximally reduced seven-variable model from the detailed elementary-step mechanism and demonstrate that it reproduces quantitatively accurately the dynamical features of the full model within a given accuracy tolerance.

Interference patterns in spiral wave drift induced by a two-point feedback

The drift velocity field describing spiral wave motion in an excitable medium subjected to a two-point feedback control is derived and analyzed. Although for a small distance between the two measuring points a discrete set of circular shaped attractors are observed, an increase of induces a sequence of global bifurcations that destroy this attractor structure. These bifurcations result in the appearance of smooth unrestricted lines with zero drift velocity, similarly to zero intensity lines under destructive interference in linear optics. The existence of such unusual equilibrium manifolds is demonstrated analytically and confirmed by computations with the Oregonator model as well as by experiments with the light-sensitive Belousov-Zhabotinsky reaction.

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)].