Photosensitive Belousov-Zhabotinsky Research Articles

Investigating the nonlinear dynamics of photosensitive Belousov-Zhabotinsky gels via bifurcation analyses.

Controlling the dynamics of active stimuli-responsive smart materials is essential to replicate the biomimetic functionalities at different length scales for a variety of biological systems-based applications. Photosensitive Belousov-Zhabotinsky (BZ) gels, powered by a nonlinear chemical oscillator, called a BZ reaction are one of the stimuli-responsive smart materials in demand due to their ability to continuously transduce chemical oscillations into mechanical deformations. The chemical oscillations in a BZ reaction and subsequent mechanical oscillations in photosensitive BZ gels occur due to the redox cycle of photosensitive ruthenium complex-based catalysts. In this work, our objective is to identify how the behavior of photosensitive BZ gels can be tuned and used for biomimetic applications by investigating its dynamical characteristics using bifurcation analyses. Specifically, we use the normal form approach and perform linear and nonlinear stability analyses to identify high-order bifurcations by computing higher-order Lyapunov and frequency coefficients. We revealed the existence of domains that encompass coexisting stable and unstable limit cycles (LCs), which merge to form a semi-stable LC at the limit point of cycle (LPC). Their existence shows how a slight variation in the BZ gel recipe can significantly alter its dynamics. Subsequently, we quantify the amplitude and frequency of oscillations in different domains under the effect of variation of BZ reaction formulations. We believe that the outcomes of our work serve as an efficient template for the design and control of BZ gel-based applications. The usage of a normal form and a systematic representation of nonlinear dynamics allow our framework to be extended for other nonlinear dynamical systems.

Real-time Mode-switching of a Self-propelled Droplet Controlled by the Photosensitive Belousov–Zhabotinsky Reaction

Variety of self-propelled droplets have been reported, which originate from interfacial chemical reactions and sometimes show sensitivity to environmental conditions. In this paper, a photosensitive Belousov–Zhabotinsky (BZ) droplet was prepared in an oil phase under illumination whose intensity changed in time. As a result, the droplet motion transited between random and oscillatory motions concurrent with the internal BZ state. The success in the real-time mode-switching reveals that separating the role is one promising strategy to realize desired functionality.

Dynamics of spiral waves and bubble formation in a closed chemical system of thin photosensitive excitable media

Spiral waves have been observed in a thin layer of excitable media. Especially, electrical spiral waves in cardiac tissues connect to cardiac tachycardia and life-threatening fibrillations. The Belousov-Zhabotinsky (BZ) reaction is the most widely used system to study the dynamics of spiral waves in experiments. When the light sensitive Ru(bpy)3 2+ is used as the catalyst, the BZ reaction becomes photosensitive and the excitability of the reaction can be controlled by varying the illumination intensity. However, the typical photosensitive BZ reaction produces many CO2 bubbles so the spiral waves are always studied in thin layer media with opened top surfaces to release the bubbles. In this work, we develop new chemical recipes of the photosensitive BZ reaction which produces less bubbles. To observe the production of bubbles, we investigate the dynamics of spiral waves in a closed thin layer system. The results show that both the speed of spiral waves and the number of bubbles increase with the concentration of sulfuric acid (H2SO4) and sodium bromate (NaBrO3). For high initial concentrations of both reactants, the size of bubbles increases with time until the wave structures are destroyed. We expect that the chemical recipes reported here can be used to study complicated dynamics of three-dimensional spiral waves in thick BZ media where the bubbles cannot escape.

Threaded Rings that Swim in Excitable Media.

Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral waves of excitation. Here we consider a novel topological configuration in which a closed filament loop, known as a scroll ring, is threaded by a pair of counterrotating filaments that are perpendicular to the plane of the ring and end on the boundary of a thin medium. We simulate the dynamics of this threaded ring (thring) in the photosensitive Belousov-Zhabotinsky excitable medium, using the modified Oregonator reaction-diffusion equations. These computations reveal that the threading topology induces an exotic motion in which the thring swims in the plane of the ring. We propose a light templating protocol to create a thring in the photosensitive Belousov-Zhabotinsky medium and provide experimental confirmation that this protocol indeed yields a thring.

Experimental Investigation of the Dynamical Modes of Four Pulse‐Coupled Chemical Micro‐Oscillators

We present an experimental system of four identical microreactors (MRs) in which the photosensitive oscillatory Belousov-Zhabotinsky (BZ) reaction occurs. The inhibitory coupling of these BZ MRs is organized via pulses of light coming to each MR from a computer projector. These pulses are induced by spike(s) in other MR(s) of the same network. Time delay between the spike in one BZ MR and the pulsed perturbation of the other BZ MR(s), the amplitude of light pulses, their duration, and the connectivity of the MRs are controlled by the LabVIEW software. Recording the dynamics of the BZ reaction in the MRs via a microscope equipped with a CCD camera, we observe all the main dynamical modes of our network of MRs, which are the IP (in-phase), AP (anti-phase), W (walk), and WR (walk reverse) for the unidirectional coupling, and the IP, two-cluster, three-cluster, and splay modes for the all-to-all coupling. Our software detects all the modes of the network automatically and makes it possible to switch between them on demand using a few special "switching" pulses. As the result of the present work, the experimental implementation of the adaptive behaviour of the pulse-coupled chemical micro-oscillator networks becomes available.

Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators.

The Belousov-Zhabotinsky (BZ) reaction is a famous experimental model for chemical oscillatory reaction and pattern formation. We herein study a diffusive coupled system of two oscillators with global feedback using the photosensitive BZ reaction both experimentally and theoretically. The coupled oscillator showed in-phase and antiphase oscillations depending on the strength of diffusive coupling and light feedback. Moreover, we analyzed our model to locate the bifurcational origin and found the reconnection of the bifurcation branches for antiphase oscillation, which was induced by the competition between global feedback and the diffusion effect.

Control of transversal instabilities in reaction-diffusion systems

In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

Dynamics of a 1D array of inhibitory coupled chemical oscillators in microdroplets with global negative feedback.

We have investigated the effect of global negative feedback (GNF) on the dynamics of a 1D array of water microdroplets (MDs) filled with the reagents of the photosensitive oscillatory Belousov-Zhabotinsky (BZ) reaction. GNF is established by homogeneous illumination of the 1D array with the light intensity proportional to the number of BZ droplets in the oxidized state with the coefficient of proportionality ge. MDs are immersed in the continuous oil phase and diffusively coupled with the neighboring droplets via inhibitor Br2 which is soluble in the oil phase. At chosen concentrations of the BZ reactants, illumination suppresses the BZ oscillators. Without GNF, or at a very small ge < 0.29, local inhibitory coupling leads to out-of-phase oscillations of the neighboring BZ droplets with an almost constant phase shift Δφ between them, which makes a space-time plot of the BZ MDs look like a staircase. At 0.3 < ge < 0.6, regular oscillatory clusters consisting of distant BZ MDs (mostly 5-6 phase clusters) emerge. At 0.6 ≤ ge ≤ 1.0, chaotic clusters are observed. At 1.2 < ge < 1.8, regular (mostly 3-4-phase) clusters emerge again. At 1.8 < ge < (3-4), complex clusters with different (but multiple) periods of oscillation are observed. At the same time, some droplets stop oscillating. At large enough ge (>4), in the region of two-phase clusters (with several suppressed BZ MDs), final patterns seem to resemble the initial patterns. Intensive computer simulations with the ordinary differential equations support experimental results.

Achilles' heel of a traveling pulse subject to a local external stimulus.

The response of a traveling pulse to a local external stimulus is considered numerically for a modified three-component Oregonator, which is a model system for the photosensitive Belousov-Zhabotinsky (BZ) reaction. The traveling pulse is traced and constantly stimulated, with the distance between the pulse and the stimulus being kept constant. We are interested in the minimal strength of the spatially localized stimulus in order to eliminate the pulse. The use of a stimulus of small width allows us to detect the point in the pulse most sensitive to the external stimulus, referred to as the "Achilles' heel" of the traveling pulse, at which minimal strength of stimulus causes a collapse of the pulse. Our findings are demonstrated experimentally as well with the photosensitive BZ reaction.

Chemical memory with states coded in light controlled oscillations of interacting Belousov-Zhabotinsky droplets.

The information storing potential of droplets, in which an oscillatory, photosensitive Belousov-Zhabotinsky (BZ) reaction proceeds, is investigated experimentally. We consider coupled oscillations in pairs and triplets of droplets. Droplets are surrounded by a solution of lipids in decane. Oscillations synchronize via diffusion of an activator through a lipid bilayer. The reaction in each droplet can be individually controlled by illumination with blue light through an optical fiber. We found that in pairs of BZ droplets, only the in-phase and the forcing oscillation modes are stable, however switching between these modes is not reliable. In triplets of droplets, switching between two different, stable rotational modes (clockwise and anticlockwise) can be easily implemented. Therefore, such a system is an excellent candidate for a light controlled, reliable, one bit chemical memory unit.

Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction.

The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10-21 L) or droplets (V ≈ [10-8-10-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.

Retrograde and Direct Wave Locomotion in a Photosensitive Self‐Oscillating Gel

AbstractCrawling motion mediated by retrograde and direct waves, that is, in the opposite or the same direction, respectively, as the muscular wave that generates it, is a fundamental mode of biological locomotion, from which more complex and sophisticated locomotion modes involving outgrowths such as limbs and wings may have evolved. A detailed general description of muscular wave locomotion and its relationship with other modes of locomotion is a challenging task. We employ a model of a photosensitive self‐oscillating gel, in which chemical pulse waves and a stimulus‐responsive medium play roles analogous to nerve pulses and deformable muscles in an animal, to generate retrograde and direct waves under non‐uniform illumination. Analysis reveals that the directional locomotion arises from a force asymmetry that results in unequal translation lengths in the push and pull regions associated with a pulse wave. This asymmetry can be modulated by the kinetic parameters of the photosensitive Belousov–Zhabotinsky reaction and the performance parameters of the gel, enabling a transition between retrograde and direct wave locomotion.

Retrograde and Direct Wave Locomotion in a Photosensitive Self-Oscillating Gel.

Crawling motion mediated by retrograde and direct waves, that is, in the opposite or the same direction, respectively, as the muscular wave that generates it, is a fundamental mode of biological locomotion, from which more complex and sophisticated locomotion modes involving outgrowths such as limbs and wings may have evolved. A detailed general description of muscular wave locomotion and its relationship with other modes of locomotion is a challenging task. We employ a model of a photosensitive self-oscillating gel, in which chemical pulse waves and a stimulus-responsive medium play roles analogous to nerve pulses and deformable muscles in an animal, to generate retrograde and direct waves under non-uniform illumination. Analysis reveals that the directional locomotion arises from a force asymmetry that results in unequal translation lengths in the push and pull regions associated with a pulse wave. This asymmetry can be modulated by the kinetic parameters of the photosensitive Belousov-Zhabotinsky reaction and the performance parameters of the gel, enabling a transition between retrograde and direct wave locomotion.

A novel technique to initiate and investigate scroll waves in thin layers of the photosensitive Belousov-Zhabotinsky reaction.

While free scroll rings are non-stationary objects that either grow or contract with time, spatial confinement can have a large impact on their evolution reaching from significant lifetime extension (J.F. Totz, H. Engel, O. Steinbock, New J. Phys. 17, 093043 (2015)) up to formation of stable stationary and breathing pacemakers (A. Azhand, J.F. Totz, H. Engel, EPL 108, 10004 (2014)). Here, we explore the parameter range in which the interaction between an axis-symmetric scroll ring and a confining planar no-flux boundary can be studied experimentally in transparent gel layers supporting chemical wave propagation in the photosensitive variant of the Belousov-Zhabotinsky medium. Based on full three-dimensional simulations of the underlying modified complete Oregonator model for experimentally realistic parameters, we determine the conditions for successful initiation of scroll rings in a phase diagram spanned by the layer thickness and the applied light intensity. Furthermore, we discuss whether the illumination-induced excitability gradient due to Lambert-Beer's law as well as a possible inclination of the filament plane with respect to the no-flux boundary can destabilize the scroll ring.

Hysteresis and drift of spiral waves near heterogeneities: From chemical experiments to cardiac simulations

Dissipative patterns in excitable reaction-diffusion systems can be strongly affected by spatial heterogeneities. Using the photosensitive Belousov-Zhabotinsky reaction, we show a hysteresis effect in the transition between free and pinned spiral rotation. The latter state involves the rotation around a disk-shaped obstacle with an impermeable and inert boundary. The transition is controlled by changes in light intensity. For permeable heterogeneities of higher excitability, we observe spiral drift along both linear and circular boundaries. Our results confirm recent theoretical predictions and, in the case of spiral drift, are further reproduced by numerical simulations with a modified Oregonator model. Additional simulations with a cardiac model show that orbital motion can also exist in anisotropic and three-dimensional systems.

Coherence Resonance of Small World Networks with Adaptive Coupling

The phenomenon of coherence resonance (CR) in small world networks with adaptive coupling is investigated by modeling a real experimental situation with a photosensitive Belousov–Zhabotinsky reaction. We show that both spatial synchronization and temporal coherence of noise-induced firings can be considerably improved by adjusting control parameters, such as the degree of connectivity and the coupling strength. A small fraction of possible long-range connections is enough to obtain a great enhancement in CR.

Experimental, numerical, and mechanistic analysis of the nonmonotonic relationship between oscillatory frequency and photointensity for the photosensitive Belousov-Zhabotinsky oscillator.

The oscillation frequency of a nonlinear reaction system acts as a key factor for interaction and superposition of spatiotemporal patterns. To control and design spatiotemporal patterns in oscillatory media, it is important to establish the dominant frequency-related mechanism and the effects of external forces and species concentrations on oscillatory frequency. In the Ru(bipy)3(2+)-catalyzed Belousov-Zhabotinsky oscillator, a nonmonotonic relationship exists between light intensity and oscillatory frequency (I-F relationship), which is composed of fast photopromotion and slow photoinhibition regions in the oscillation frequency curve. In this work, we identify the essential mechanistic step of the I-F relationship: the previously proposed photoreaction Ru(II)* + Ru(II) + BrO3(-) + 3H(+) → HBrO2 + 2Ru(III) + H2O, which has both effects of frequency-shortening and frequency-lengthening. The concentrations of species can shift the light intensity that produces the maximum frequency, which we simulate and explain with a mechanistic model. This result will benefit studies of pattern formation and biomimetic movement of oscillating polymer gels.

Three-dimensional autonomous pacemaker in the photosensitive Belousov-Zhabotinsky medium

In experiments with the photosensitive Belousov-Zhabotinsky reaction (PBZR) we found a stable three-dimensional organizing center that periodically emits trigger waves of chemical concentration. The experiments are performed in a parameter regime with negative line tension using an open gel reactor to maintain stationary non-equilibrium conditions. The observed periodic wave source is formed by a scroll ring stabilized due to its interaction with a no-flux boundary. Sufficiently far from the boundary, the scroll ring expands and undergoes the negative line tension instability before it finally develops into scroll wave turbulence. Our experimental results are reproduced by numerical integration of the modified Oregonator model for the PBZR. Stationary and breathing self-organized pacemakers have been found in these numerical simulations. In the latter case, both the radius of the scroll ring and the distance of its filament plane to the no-flux boundary after some transient undergo undamped stable limit cycle oscillations. So far, contrary to their stationary counterpart, the numerically predicted breathing autonomous pacemaker has not been observed in the chemical experiment.

Traveling spots and traveling fingers in singular limit problems of reaction-diffusion systems

In this study, we consider the traveling spots that were observed in the photosensitive Belousov-Zhabotinsky reaction experiment conducted by Mihailuk et al. in 2001. First, we introduce the interface equation by the singular limit analysis of a FitzHugh--Nagumo-type reaction-diffusion system. Then, we obtain the profile of the support of the solution. Next, we prove the uniqueness of the traveling spot by studying ordinary differential equations that describe its front and back. In addition, we provide an upper bound for the width of the spot. Furthermore, we compare the singular limit problem with the wave front interaction model proposed by Zykov and Showalter in 2005 and obtain traveling fingers.

Effect of Noise Correlation on Noise-Induced Oscillation Frequency in the Photosensitive Belousov–Zhabotinsky Reaction in a Continuous Stirred Tank Reactor

We report on the experimental study of noise-induced oscillations in the photosensitive Ru(bpy)3(2+)-catalyzed Belousov-Zhabotinsky reaction in a continuous stirred tank reactor (CSTR). In the absence of deterministic oscillations and any external periodic forcing, oscillations appear when the system is perturbed by stochastic fluctuations in light irradiation with sufficiently high amplitude in the vicinity of the bifurcation point. The frequency distribution of the noise-induced oscillations is strongly affected by noise correlation. There is a shift of the noise-induced oscillation frequency toward higher frequencies for an intermediate range of the noise correlation exponent, indicating the occurrence of coherence resonance. Our findings indicate that, in principle, noise correlation can be used to direct chemical reactions toward certain behavior.