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This review summarizes recent studies on the catalytic CO oxidation on Iridium(111) surfaces. This was investigated experimentally under ultrahigh vacuum (UHV) conditions using mass spectroscopy to detect gaseous products and photoelectron emission microscopy (PEEM) to visualize surface species. The underlying reaction–diffusion system based on the Langmuir–Hinshelwood mechanism was analyzed numerically.

The existence of bistability for this surface reaction was shown in experiment. For the first time the effect of noise on a bistable surface reaction was examined. In a surface science experiment the effects on product formation and the development of spatio-temporal patterns on the surface were explored.

Steady state CO₂ rates were measured under constant flux of the CO + O mixture as a function of sample temperature (360 K < T < 700 K) and gas composition, characterized by the molar fraction of CO in the feed gas (0 ≤ Y ≤ 1). The reaction reveals bistability in a limited region of Y and T. A rate hysteresis with two steady state rates was observed for cycling Y up and down, one of high reactivity (upper rate, oxygen covered surface) and one of low reactivity (lower rate, CO covered surface). The position of the hysteresis loop shifts to higher Y values and decreases in width with increasing temperature. For small CO content in the feed gas the CO₂ rate is proportional to Y^3/2. At 500 K extremely slow Y cycling measurements (about 100 hours per direction) were done and showed that bistability still exists and no slowly changing transients were observed. The requirements for the speed with which experiments can be executed without producing experimental artifacts were explored. Since over-sampling alters the measured hysteresis loop, a maximum rate for changing the gas composition in Y cycling experiments was determined.

The influence of noise on the reaction rates and the formation of spatio-temporal patterns on the surface was explored by superposing noise of Gaussian white type on Y and on T. Noisy Y (deviation Δ Y) represents multiplicative and additive noise, noisy T (deviation Δ T) multiplicative noise only. Noisy T enters the reaction via the rate-determining step, the observed CO₂ rates become noisy for low temperatures (around 420 K) when the surface is dominantly oxygen covered (CO + O reaction step is rate-limiting) and for higher temperatures (around 500 K) when the surface is dominantly CO covered (CO desorption step is rate-limiting).

The effect of noisy Y was examined for a sample temperature of 500 K and is dependent on the selected average gas composition. In the regions with one steady state CO₂ rate (outside the hysteresis) the recorded rates were noisy. The probability distribution of the rates is Gaussian shaped for the upper rate (below hysteresis) and asymmetric for the lower rate (above hysteresis). For large noise strength bursts, short-time excursions to and above the upper rate, were observed.

Inside the hysteresis small noise made the steady state rates noisy, but above a Y-dependent Δ Y transients from the locally stable to the globally stable rate branch were observed. These transients take up to several ten thousand seconds and become faster with increasing noise. For larger Y noise strength bursts and switching between both steady state rates were detected.

Photoelectron emission microscopy (PEEM) was done to visualize spatio-temporal adsorbate patterns on the surface as expected from the observations in the CO₂ rate measurements. CO- and oxygen-covered regions on the Ir(111) surface are visible in PEEM images as gray and black areas as a consequence of their work function contrast. Islands of the adsorbate, corresponding to the globally stable branch, are formed in a background of the other one. The long transient times are the result of the extremely slow domain wall motion of these islands (around 0.05 μm s^-1). In the hysteresis region CO oxidation on Iridium(111) surfaces is dominated by domain formation and wall motion for small to moderate noise strength. The island density increases with noise, but the wall velocity is independent of applied Δ Y. For larger noise amplitudes, fast switching between oxygen- and CO-dominated surfaces is observed as well as nucleation and growth of the minority phase in the majority phase.

In the numerically analyzed reaction–diffusion system all parameters were taken from the experiment. Modeling the reaction–diffusion system shows qualitative up to quantitative agreement with the experimental observations. The length scale for the modeling grid is determined from wall velocity seen in the experiments.

This paper presents a detailed analysis on the dynamics of a ring network with short-cut. We first investigate the absolute synchronization on the basis of Lyapunov stability approach, and then discuss the linear stability of the trivial solution by analyzing the distribution of zeros of the characteristic equation. Based on the equivariant branching lemma, we not only obtain the existence of primary steady state bifurcation but also analyze the patterns and stability of the bifurcated nontrivial equilibria. Moreover, by means of the equivariant Hopf bifurcation theorem, we not only investigate the effect of connection strength on the spatio-temporal patterns of periodic solutions emanating from the trivial equilibrium, but also derive the formula to determine the direction and stability of Hopf bifurcation. In particular, we further consider the secondary bifurcation of the nontrivial equilibria. These studies show that short-cut may be used as a simple but efficient switch to control the dynamics of a system.

The bloom of toxin producing phytoplankton (TPP) is an environmental issue due to its negative impact on fresh water and marine ecology. In this paper, such a phenomenon is modeled using the reaction–diffusion equations. The spatiotemporal interaction among non-toxin producing phytoplankton (NTP), TPP, and zooplankton has been considered with Holling type II and III functional responses. The stability analysis for non-spatial and spatial model system is carried out and numerical simulations are performed for a fixed set of parameter values, which is realistic to planktonic dynamics. It has been observed that on increasing the reduction rate of zooplankton, the system shows cyclic to stable behavior. The result shows that the predators which avoid to toxic prey promote the bloom. Non-Turing patchy pattern has also been observed on time evolution. In this work, we have taken the case study of Sundarban mangrove wetland which is suffering from algal bloom due to the presence of toxic Dinoflagellates and Cyanophyceae. Through the numerical simulation, it has been shown that the higher value of reduction rate of zooplankton (${\xi }_2$) is responsible for bad health of the wetland system.

The effect of Gaussian white noise on a chemical wavefront is studied in a modified FitzHugn–Nagumo model by applying numerical simulations. A rotating spiral waves can be formed if the medium is excitable enough and the fronts has a free end, when the reaction diffusion system is disturbed by a certain non-zero level noise. It is counterintuitive that noise plays a constructive role in the product and propagation of single spiral waves in this letter. Weak or strong noise will make against the product and propagation of spiral waves. In a certain noise level, spiral wave can be maintained in a medium, where such spiral waves cannot be observed in the absence of the noise.