Related papers: Pattern dynamics of the nonreciprocal Swift-Hohenb…

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…

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.…

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…

Computational modeling of pattern formation in nonequilibrium systems is a fundamental tool for studying complex phenomena in biology, chemistry, materials science and engineering. The pursuit for theoretical descriptions of some among…

We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary,…

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…

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…

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…

Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

Critical transitions are of great interest to scientists in many fields. Most knowledge about these transitions comes from systems exhibiting the multistability of spatially uniform states. In spatially extended and, particularly, in…

A diffusive ratio-dependent Holling-Tanner system subject to Neumann boundary conditions is considered. The existence of multiple bifurcations, including Turing-Hopf bifurcation, Turing-Truing bifurcation, Hopf-double-Turing bifurcation and…

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…

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective…

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…

We numerically investigate the characteristics of the long-time dynamics of a single-site wave-packet excitation in a disordered and nonlinear Su-Schrieffer-Heeger model. In the linear regime, as the parameters controlling the topology of…

A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…

We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation long-wave and short-wave patterns with length scales related as…

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…

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…