Related papers: Instabilities and Patterns in Coupled Reaction-Dif…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
We analyze an unusual class of bosonic dynamical instabilities that arise from dissipative (or non-Hermitian) pairing interactions. We show that, surprisingly, a completely stable dissipative pairing interaction can be combined with simple…
We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function…
In this paper we provide detailed information about the instability of equilibrium solutions of a nonlinear family of localized reaction-difussion equations in dimensione one. Beyond we provide explicit formulas to the equilibrium…
In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady-states, providing a rare generic organizing principle for far-from-equilibrium…
I show stable, localized, single and multi-spot patterns of three classes - stationary, moving, and rotating - that exist within a limited range of parameter values in the two-dimensional Gray-Scott reaction-diffusion model with ${\sigma} =…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
Vesicles are important surrogate structures made up of multiple phospholipids and cholesterol distributed in the form of a lipid bilayer. Tubular vesicles can undergo pearling i.e., formation of beads on the liquid thread akin to the…
In a Vlasov equation, the destabilization of a homogeneous stationary state is typically described by a continuous bifurcation characterized by strong resonances between the unstable mode and the continuous spectrum. However, when the…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
This paper is devoted to reaction-diffusion equations with bistable nonlinearities depending periodically on time. These equations admit two linearly stable states. However, the reaction terms may not be bistable at every time. These may…
A reaction-diffusion-advection predator-prey model with Holling type-II predator functional response is considered. We show the stability/instability of the positive steady state and the existence of a Hopf bifurcation when the diffusion…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…
We study, analytically and numerically, the stationary states in the system of two linearly coupled nonlinear Schr{\"o}dinger equations in two spatial dimensions, with the nonlinear interaction coefficients of opposite signs. This system is…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
A chemotaxis-diffusion-convection coupling system for describing a form of buoyant convection in which the fluid develops convection cells and plume patterns will be investigated numerically in this study. Based on the two-dimensional…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…
We analyze the stability and bifurcation structure of steady states in a mechanochemical model of pattern formation in regenerating tissue spheroids. The model couples morphogen dynamics with tissue mechanics via a positive feedback loop:…