Instability of the Homogeneous Distribution of Chemical Waves in the Belousov–Zhabotinsky Reaction

Chemical traveling waves play an important role in biological functions, such as the propagation of action potential and signal transduction in the nervous system. Such chemical waves are also observed in inanimate systems and are used to clarify their fundamental properties. In this study, chemical waves were generated with equivalent spacing on an excitable medium of the Belousov–Zhabotinsky reaction. The homogeneous distribution of the waves was unstable and low- and high-density regions were observed. In order to understand the fundamental mechanism of the observations, numerical calculations were performed using a mathematical model, the modified Oregonator model, including photosensitive terms. However, the homogeneous distribution of the traveling waves was stable over time in the numerical results. These results indicate that further modification of the model is required to reproduce our experimental observations and to discover the fundamental mechanism for the destabilization of the homogeneous-distributed chemical traveling waves.

Bifurcation dynamics in a fractional-order oregonator model including time delay

Setting up mathematical models to describe the interaction of chemical variables has been a hot issue in chemical and mathematical areas. Nevertheless, many mathematical models are only involved with the integer-order differential equation case. The fruits on fractional-order chemical models are very scarce. In this present work, on the basis of the previous studies, we set up a novel fractional-order delayed Oregonator model. Selecting the time delay as bifurcation parameter, we obtain novel delay-independent bifurcation conditions that guarantee the stability and the appearance of Hopf bifurcation for the fractional-order delayed Oregonator model. The study shows that time delay plays a vital role in controlling the stability and the appearance of Hopf bifurcation of the considered fractional-order delayed Oregonator model. In order to verify the rationality of theoretical results, computer simulations are carried out.

Study on the Formation of Complex Chemical Waveforms by Different Computational Methods

Chemical wave is a special phenomenon that presents periodic patterns in space-time domain, and the Belousov–Zhabotinsky (B-Z) reaction is the first well-known reaction-diffusion system that exhibits organized patterns out of a homogeneous environment. In this paper, the B-Z reaction kinetics is described by the Oregonator model, and formation and evolution of chemical waves are simulated based on this model. Two different simulation methods, partial differential equations (PDEs) and cellular automata (CA) are implemented to simulate the formation of chemical waveform patterns, i.e., target wave and spiral wave on a two-dimensional plane. For the PDEs method, reaction caused changes of molecules at different location are considered, as well as diffusion driven by local concentration difference. Specifically, a PDE model of the B-Z reaction is first established based on the B-Z reaction kinetics and mass transfer theory, and it is solved by a nine-point finite difference (FD) method to simulate the formation of chemical waves. The CA method is based on system theory, and interaction relations with the cells nearest neighbors are mainly concerned. By comparing these two different simulation strategies, mechanisms that cause the formation of complex chemical waves are explored, which provides a reference for the subsequent research on complex systems.

BASIC CONCEPTS OF SELF-ORGANIZED PHENOMENA IN CHEMICAL SYSTEMS

We present the main concepts of nonlinear dynamics and thermodynamics of irreversible processes to introduce chemistry students to the topic of self-organized phenomena. This task is performed by theoretically describing the emergence of self-sustained oscillations, waves, and stationary patterns/Turing patterns in the Belousov-Zhabotinsky (BZ) reaction, through the Oregonator model. We carefully developed such a description, which resulted in long algebraic deductions and rich supplementary material. Considering that, we encourage the use of this material in undergraduate and graduate advanced physical chemistry classes.

Exploration of Light-Controlled Chemical Behavior and Mechanism in a Macrocyclic Copper Complex Catalyst–Acetone–Glucose–Bromate–Sulfuric Acid Oscillation System

In this paper, the effect of ultraviolet light on the [CuL](ClO4)2–glucose (Glu)–acetone (Act)–sodium bromate (NaBrO3)–sulfuric acid (H2SO4) oscillation system was studied. The reaction mechanism and Oregonator model were established to verify the mechanism. Comparison of the bromide ion electrode–platinum electrode correlation diagrams with and without ultraviolet light reveals a nontracking phenomenon in the bromide ion electrode–platinum electrode correlation diagram under illumination, indicating that the illumination will affect the changes in the bromide ion concentration in the system. During the process, as UV intensity increases, the concentration of bromide ions in the system increases, and bromide ions can inhibit chemical oscillations, resulting in a decrease in the amplitude of chemical oscillations, further verifying that the proposed mechanism is reasonable.

Cellular Automaton Belousov–Zhabotinsky Model for Binary Full Adder

The continuous increment in the performance of classical computers has been driven to its limit. New ways are studied to avoid this oncoming bottleneck and many answers can be found. An example is the Belousov–Zhabotinsky (BZ) reaction which includes some fundamental and essential characteristics that attract chemists, biologists, and computer scientists. Interaction of excitation wave-fronts in BZ system, can be interpreted in terms of logical gates and applied in the design of unconventional hardware components. Logic gates and other more complicated components have been already proposed using different topologies and particular characteristics. In this study, the inherent parallelism and simplicity of Cellular Automata (CAs) modeling is combined with an Oregonator model of light-sensitive version of BZ reaction. The resulting parallel and computationally-inexpensive model has the ability to simulate a topology that can be considered as a one-bit full adder digital component towards the design of an Arithmetic Logic Unit (ALU).

Fredkin and Toffoli Gates Implemented in Oregonator Model of Belousov–Zhabotinsky Medium

A thin-layer Belousov–Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates — Fredkin gate and Toffoli gate — in a BZ medium network of excitable channels with subexcitable junctions. Local control of the BZ medium excitability is an important feature of the gates’ design. An excitable thin-layer BZ medium responds to a localized perturbation with omnidirectional target or spiral excitation waves. A subexcitable BZ medium responds to an asymmetric perturbation by producing traveling localized excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform the computation. We interpret the wave-fragments as values of Boolean variables. The presence of a wave-fragment at a given site of a circuit represents the logical truth, absence of the wave-fragment — logically false. Fredkin gate consists of ten excitable channels intersecting at 11 junctions, eight of which are subexcitable. Toffoli gate consists of six excitable channels intersecting at six junctions, four of which are subexcitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.

On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D

The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the Oregonator model are derived using the method of Darboux polynomials. It is shown that, the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model can be written in a bi-Hamiltonian/Nambu metriplectic form.