Related papers: Domain formation in transitions with noise and tim…
The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or…
We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial…
We propose general conditions for the emergence of Turing patterns in a domain that changes size through homogeneous growth/shrinkage based on the qualitative changes of a potential function. For this part of the work, we consider the most…
Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase equation, the interaction of such walls is…
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established.…
Spatial pattern formation in excitable fluctuating media was researched analytically from the point of view of the order parameters concept. The reaction-diffusion system in external noise is considered as a model of such medium. Stochastic…
We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…
The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of…
We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
We investigate the pattern dynamics of the one-dimensional nonreciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns such as disordered, aligned, swap, chiral-swap, and chiral phases emerge depending on the parameters. We…
A dynamic symmetry-breaking transition with noise and inertia is analyzed. Exact solution of the linearized equation that describes the critical region allows precise calculation (exponent and prefactor) of the number of defects produced as…
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…
The formation of topological defects in second-order phase transitions can be investigated by solving partial differential equations for the evolution of the order parameter in space and time, such as the Langevin equation. We demonstrate…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized…
Spatial and temporal noise power spectra of stripe patterns are investigated, using as a model a Swift-Hohenberg equation with a stochastic term. In particular, the analytical and numerical investigations show: 1) the temporal noise spectra…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
We consider the approximation via modulation equations for nonlinear SPDEs on unbounded domains with additive space time white noise. Close to a bifurcation an infinite band of eigenvalues changes stability, and we study the impact of small…