Related papers: Formation and Persistence of Spatiotemporal Turing…
In this paper, we investigate the emergence of a predator-prey system with Ivlev-type functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the…
In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is…
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to…
Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model,…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
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…
Striped Turing patterns and solitary band and disk structures are constructed using a three-variable multiscale model with cubic nonlinearity and global control. The existence and stability conditions of regular structures are analysed…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
In this paper we present a study of pattern formation in bidimensional systems with competing short-range attractive and long-range repulsive interactions. The interaction parameters are chosen in such a way to analyse two different…
Morphogenetic patterns are highly sophisticated dissipative structures. Are they governed by the same general mechanisms as chemical and hydrodynamic patterns? Turing's symmetry breaking and Wolpert's signalling provide alternative…