相关论文: Tristability between stripes, up-, and down-hexago…

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…

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 study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number $k\approx 1$ bifurcate supercritically from the zero state and form…

In some pattern-forming systems, for some parameter values, patterns form with two wavelengths, while for other parameter values, there is only one wavelength. The transition between these can be organised by a codimension-three point at…

In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…

We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in…

Spatio-temporal pattern formation in complex systems presents rich nonlinear dynamics which leads to the emergence of periodic nonequilibrium structures. One of the most prominent equations for the theoretical and numerical study of the…

Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical and biological media and to macro-scale vegetation and cloud patterns. Their…

We study the existence of patterns (nontrivial, stationary solutions) for one-dimensional Swift-Hohenberg Equation in a directional quenching scenario, that is, on $x\leq 0$ the energy potential associated to the equation is bistable,…

Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…

Breaking the chiral symmetry, rotation induces a secondary Hopf bifurcation in weakly nonlinear hexagon patterns which gives rise to oscillating hexagons. We study the stability of the oscillating hexagons using three coupled…

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.…

We revisit the Swift-Hohenberg model for two-dimensional hexagonal patterns in the bistability region where hexagons coexist with the uniform quiescent state. We both analyze the law of motion of planar interfaces (separating hexagons and…

We apply analytical and numerical methods to study the linear stability of stripe patterns in two generalizations of the two-dimensional Swift-Hohenberg equation that include coupling to a mean flow. A projection operator is included in our…

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…

The Swift-Hohenberg equation is ubiquitous in the study of bistable dynamics. In this paper, we study the dynamic transitions of the Swift-Hohenberg equation with a third-order dispersion term in one spacial dimension with a periodic…

When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…

We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls…

We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems…

This paper addresses the existence and spectral stability of traveling fronts for nonlinear hyperbolic equations with a positive "damping" term and a reaction function of bistable type. Particular cases of the former include the relaxed…