Related papers: Spatiotemporal pattern formation in a three-variab…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
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…
This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold…
The turn-over frequency of the catalytic oxidation of CO at RuO2(110) was calculated as function of temperature and partial pressures using ab initio statistical mechanics. The underlying energetics of the gas-phase molecules, dissociation,…
Spatiotemporal pattern formation in a product-activated enzymic reaction at high enzyme concentrations is investigated. Stochastic simulations show that catalytic turnover cycles of individual enzymes can become coherent and that complex…
The formation mechanisms of aromatic compounds in flame are strongly influenced by the chemical and thermal history that leads to their formation. Indeed, the complex environments that characterize combustion systems do not only affect the…
Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…
Spatiotemporal localized and extended structures associated with a subcritical finite wavenumber Hopf bifurcation are studied in the Purwins model (a three-variable FitzHugh-Nagumo version). Steady and time-dependent numerical continuation…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
The effects of a spatially periodic forcing on an oscillating chemical reaction as described by the Lengyel-Epstein model are investigated. We find a surprising competition between two oscillating patterns, where one is harmonic and the…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…
We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker-Doering equations, in which clusters grow or shrink by…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
The memory-based diffusion systems have wide applications in practice. Hopf bifurcations are observed from such systems. To meet the demand for computing the normal forms of the Hopf bifurcations of such systems, we develop an effective new…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…