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Extensive simulations are performed of the diffusion-limited reaction A$+$B$\to 0$ in one dimension, with initially separated reagents. The reaction rate profile, and the probability distributions of the separation and midpoint of the…

Condensed Matter · Physics 2009-10-22 Stephen Cornell

Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 D. Ryvkine , M. I. Dykman , B. Golding

Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…

Dynamical Systems · Mathematics 2018-11-27 Yanfei Du , Ben Niu , Yuxiao Guo , Junjie Wei

In a two species reaction diffusion system,we show that it is possible to generate a set of wavelength doubling bifuractions leading to spatially chaotic state.The wavelength doubling bifurcations are preceded by a symmetry breaking…

Statistical Mechanics · Physics 2007-05-23 Deepak Kar , J K Bhattacharjee

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a…

Pattern Formation and Solitons · Physics 2008-10-22 Damia Gomila , Adrian Jacobo , Manuel A. Matias , Pere Colet

The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time…

Statistical Mechanics · Physics 2009-10-30 B. Chopard , M. Droz , J. Magnin , Z. Racz

In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…

Dynamical Systems · Mathematics 2018-01-11 Wakil Sarfaraz , Anotida Madzvamuse

In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, producing a solution that concentrates at a…

Pattern Formation and Solitons · Physics 2015-09-22 Philippe H. Trinh , Michael J. Ward

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B -> 2B) and a cubic (A + 2B -> 3B) autocatalysis. The parameters of this system are the…

patt-sol · Physics 2009-10-30 Stephane Focant , Thierry Gallay

We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…

Analysis of PDEs · Mathematics 2023-10-23 Montie Avery

Fronts propagating in two-dimensional advection-reaction-diffusion (ARD) systems exhibit rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We…

Pattern Formation and Solitons · Physics 2018-03-14 Rory A. Locke , John R. Mahoney , Kevin A. Mitchell

This paper considers new approach to control a stationary inhomogeneous planar front solution of a nonlinear parabolic two-dimensional distributed (reaction-diffusion) system, by using a gain point-sensor control with actuators that have…

Optimization and Control · Mathematics 2007-05-23 Yelena Smagina , Moshe Sheintuch

We revisit the problem of pinning a reaction-diffusion front by a defect, in particular by a reaction-free region. Using collective variables for the front and numerical simulations, we compare the behaviors of a bistable and monostable…

Pattern Formation and Solitons · Physics 2021-03-31 Jean-Guy Caputo , Gustavo Cruz-Pacheco , Benoit Sarels

Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…

patt-sol · Physics 2009-10-22 John E. Pearson

We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…

Pattern Formation and Solitons · Physics 2019-10-21 Daniel Gomez

We investigate the influence of a stochastically fluctuating step-barrier potential on bimolecular reaction rates by exact analytical theory and stochastic simulations. We demonstrate that the system exhibits a new resonant reaction…

Chemical Physics · Physics 2016-03-23 Jakob J. Kolb , Stefano Angioletti-Uberti , Joachim Dzubiella

The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the…

Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…

Chaotic Dynamics · Physics 2015-05-28 Vladimir Klinshov , Leonhard Lücken , Dmitry Shchapin , Vladimir Nekorkin , Serhiy Yanchuk

This is a study of front dynamics in reaction diffusion systems near Nonequilibrium Ising-Bloch bifurcations. We find that the relation between front velocity and perturbative factors, such as external fields and curvature, is typically…

patt-sol · Physics 2009-10-28 Christian Elphick , Aric Hagberg , Ehud Meron

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…

Pattern Formation and Solitons · Physics 2015-06-03 Anne J. Catlla , Amelia McNamara , Chad M. Topaz