Related papers: Turing Instability and Pattern Formation in an Act…
In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the…
The existence and stability of localized patterns of criminal activity are studied for the reaction-diffusion model of urban crime that was introduced by Short et. al. [Math. Models. Meth. Appl. Sci., 18, Suppl. (2008), pp. 1249--1267].…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…
Striped patterns are known to bifurcate in reaction-diffusion systems with differential isotropic diffusions at a supercritical Turing instability. In this paper we study the impact of weak anisotropy by directional advection on the…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…
We numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is…
We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \mapsto -x$. This system exhibits a Turing instability and we…
Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an…
Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear…
We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above…
We derive a theoretical model for the Rayleigh-Taylor (RT)-like instability for a thin foil accelerated by an intense laser, taking into account finite wavelength effects in the laser wave field. The latter leads to the diffraction of the…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances…
A model for polar filaments interacting via molecular motor complexes is investigated which exhibits bifurcations to spatial patterns. It is shown that the homogeneous distribution of filaments, such as actin or microtubules, may become…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…