Lingfa Yang

Pattern formation arising from interactions between Turing and wave instabilities

We study pattern formation arising from the interaction of the stationary Turing and wave (oscillatory Turing) instabilities. Interaction and competition between these symmetry-breaking modes lead to the emergence of a large variety of spatiotemporal patterns, including modulated Turing structures, modulated standing waves, and combinations of Turing structures and spiral waves. Spatial resonances are obtained near codimension-two Turing-wave bifurcations. Far from bifurcation lines, we obtain inwardly propagating spiral waves with Turing spots at their tips. We demonstrate that the coexistence of Turing spots and traveling waves is a result of interaction between Turing and oscillatory modes, while the inwardly propagating waves (antispirals) do not require this interaction; they can arise from the wave instability combined with a negative group velocity.

Stochastic resonance in the absence and presence of external signals for a chemical reaction

A catalytic reduction of NO with CO on Pt(100) surface is adopted to study its response under random perturbation. Noise-induced oscillations and noise-induced frequency shifts have been observed when the system works in the vicinity of the oscillatory region and meanwhile is subjected to random modulation of its feeding speed. Stochastic resonance behavior can be recognized from the noise-induced peak in the power spectrum even though in the absence of external signals. The numerical results have been obtained near supercritical Hopf bifurcation points, but are not confined to the classification of bifurcation. When the system falls into bistable regions, noise can help an external weak signal to induce state-to-state transitions and also shows a stochastic resonance behavior except for the case that the system has an isolated bifurcation scheme.

Turing patterns beyond hexagons and stripes.

The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive reaction-diffusion system. The superlattices develop from initial conditions created by illuminating the system through a mask consisting of a simple hexagonal or square lattice with a wavelength close to a multiple of the intrinsic Turing patterns wavelength. We show that interaction of the photochemical periodic forcing with the Turing instability generates multiple spatial harmonics of the forcing patterns. The harmonics situated within the Turing instability band survive after the illumination is switched off and form superlattices. The square superlattices are the first examples of time-independent square Turing patterns. We also demonstrate that in a system where the Turing band is slightly below criticality, spatially uniform internal or external oscillations can create oscillating square patterns.

Advanced Reaction-Diffusion Models for Texture Synthesis

Since the introduction of texture synthesis using a reaction-diffusion model in the early 1990s, their use has not been widespread. This is likely due to both the difficulty in selecting parameters that result in stable, useful patterns as well as the computational costs of producing these patterns. In this paper we present techniques that help overcome the difficult parameter selection process that controls the pattern development. In addition, we expand the basic diffusion model to allow for shaped patterns. Finally, we show that it is possible to create multiple and oscillating patterns by coupling two reaction-diffusion systems together. These techniques have been implemented using both explicit and semi-implicit solutions on a CPU and GPU.We provide sample source code of both implementations online.

Stochastic resonance in catalytic reduction of NO with CO on Pt(100)

This paper presents a stochastic resonance occurring in a chemical reaction Pt(100)/NO+CO. The results were from numerical simulation of the nonlinear kinetic behavior of a three-variable reaction model obtained from the law of mass actions. The model exhibits a special region in the bifurcation scheme, where a stable node coexists with a stable limit cycle. When one of the control parameters is perturbed by a weak, low frequency periodic signal riding on a suitable external noisy background, transitions between the steady state and oscillatory state may become regular unexpectedly, and signal to noise ratio is thus enhanced at the signal frequency in the Fourier transform power spectrum of the time series output. That refers to stochastic resonance, in which the noise may play a constructive role in the detection of weak signals. The findings may suggest a new method to develop chemical sensitive devices in the field of applications. The paper also discusses the conditions of occurrence of stochastic res...

Stochastic resonance in surface catalytic oxidation of carbon monoxide

Stochastic resonance is a nonlinear cooperative effect between external signal and noise, in which the noise can play a constructive role to increase the signal-to-noise ratio in the detection of a weak signal. A surface catalytic reaction model, to describe oxidization of carbon monoxide carrying out far from equilibrium, was adopted to study the stochastic resonance. By computer simulation, we found noise can induce state-to-state transitions, and stochastic resonance behavior may appear at narrow bistable states or near discontinuous Hopf bifurcations, while a weak periodic signal riding on noise is input controlling.

Stochastic bi-resonance without external signal in the CO+O2 catalytic oxidation reaction system

The noisy dynamic behavior of a surface catalytic reaction model to describe the oxidation of carbon monoxide is investigated when the control parameter is perturbed by external noise near a supercritical Hopf bifurcation point. Noise induced coherent oscillation (NICO) is observed and the NICO strength goes through two maxima with the increment of the noise intensity D from zero, characteristic of the occurrence of stochastic multiresonance without external signal. The frequency of the NICO also increases with the increment of D.

Coupled and forced patterns in reaction-diffusion systems

Several reaction–diffusion systems that exhibit temporal periodicity when well mixed also display spatio-temporal pattern formation in a spatially distributed, unstirred configuration. These patterns can be travelling (e.g. spirals, concentric circles, plane waves) or stationary in space (Turing structures, standing waves). The behaviour of coupled and forced temporal oscillators has been well studied, but much less is known about the phenomenology of forced and coupled patterns. We present experimental results focusing primarily on coupled patterns in two chemical systems, the chlorine dioxide–iodine–malonic acid reaction and the Belousov–Zhabotinsky reaction. The observed behaviour can be simulated with simple chemically plausible models.

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.

Noise-induced phase transition of the dimer-monomer (DM) reaction model

Abstract Considering the gas-phase fluctuations in the Monte Carlo simulation, we construct a stochastic differential equation and the corresponding Fokker-Planck equation to describe the state evolution of the dimer-monomer (DM) surface reaction model. We find that the well-known first-order irreversible phase transition characteristic of the DM model may be viewed as a noise-induced transition.