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A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Strong, scale-free disorder disrupts typical transport properties like the Stokes-Einstein relation and linear response, leading to anomalous, non-diffusive motion observed in amorphous materials, glasses, living cells, and other systems.…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and…
The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics…
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…
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the…
Disordered systems form one of the centrestages of research in many body sciences and lead to a plethora of interesting phenomena and applications. A paradigmatic disordered system consists of an one-dimensional array of quantum spin-1/2…
We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second order…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
Symmetries rigidly delimit the landscape of quantum matter. Recently uncovered spatially modulated symmetries, whose actions vary with position, enable excitations with restricted mobility, while Lieb-Schultz-Mattis (LSM) type anomalies…
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their analysis is challenging as techniques such as spatial dynamics…
We report on self-induced switchings between multiple distinct space--time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
We investigate the possibility of projecting low dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship…
Pattern formation in biological, chemical and physical problems has received considerable attention, with much attention paid to dissipative systems. For example, the Ginzburg--Landau equation is a normal form that describes pattern…
Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of information and the transmission machinery induce…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select a specific translate of the striped patterns and induce…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…