Related papers: Snaking and isolas of localised states in bistable…
We prove a well-posedness result for stochastic Allen-Cahn type equations in a bounded domain coupled with generic boundary conditions. The (nonlinear) flux at the boundary aims at describing the interactions with the hard walls and is…
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the…
Spatially extended patterns and multistability of possible different states is common in many ecosystems, and their combination has an important impact on their dynamical behaviours. One potential combination involves tristability between a…
We introduce and experimentally demonstrate a class of surface bound states with algebraic decay in a one-dimensional tight-binding lattice. Such states have an energy embedded in the spectrum of scattered states and are structurally stable…
We study interfaces in an Allen-Cahn equation, separating two metastable states. Our focus is on a directional quenching scenario, where a parameter renders the system bistable in a half plane and monostable in its complement, with the…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one…
We study equilibria in domains with boundaries for a first-order aggregation model that includes social interactions and exogenous forces. Such equilibrium solutions can be connected or disconnected, the latter consisting in a delta…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
We study existence and stability of stationary solutions of a system of semilinear parabolic partial differential equations that occurs in population genetics. It describes the evolution of gamete frequencies in a geographically structured…
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of…
In the present work we examine both the linear and nonlinear properties of two related PT-symmetric systems of the discrete nonlinear Schrodinger (dNLS) type. First, we examine the parameter range for which the finite PT-dNLS chains have…
Coupled cell systems are dynamical systems associated to a network and synchrony subspaces, given by balanced colorings of the network, are invariant subspaces for every coupled cell systems associated to that network. Golubitsky and…
In this paper we analyze the existence, stability, dynamical formation and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schr\"{o}dinger equation with a linear point defect. We…
We introduce a model which gives rise to self-trapping of fundamental and higher-order localized states in a one-dimensional nonlinear Schr\"odinger equation with fractional diffraction and the strength of the self-defocusing nonlinearity…
In this paper, we study theoretically the emergence of localized states of vegetation close to the onset of desertification. These states are formed through the locking of vegetation fronts, connecting a uniform vegetation state with a bare…
Using Landau-de Gennes theory to describe nematic order, we study a frustrated cell consisting of nematic liquid crystal confined between two parallel plates. We prove the uniqueness of equilibrium states for a small cell width. Letting the…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving that unsymmetric collocation matrices with Thin-Plate…