Related papers: Symmetry-Breaking Bifurcations for Compartmental R…
We investigate a nonlocal single-species reaction-diffusion-advection model that integrates the spatial memory of previously visited locations and nonlocal detection in space, resulting in a coupled PDE-ODE system reflective of several…
Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between atoms. The models are based on systems of…
The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular…
We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODE's) for the dynamics of the governing…
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…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
We study static properties of disk-shaped binary dipolar Bose-Einstein condensates of $^{168}$Er-$^{164}$Dy and $^{52}$Cr-$^{164}$Dy mixtures under the action of inter- and intra-species contact and dipolar interactions and demonstrate the…
In this article, we study a system of reaction-diffusion equations in which the diffusivities are widely separated. We report on the discovery of families of spatially periodic canard solutions that emerge from {\em singular Turing…
It is known that stable 2D solitons of the semi-vortex (SV) and mixed-mode (MM) types are maintained by the interplay of the cubic attractive nonlinearity and spin-orbit coupling (SOC) in binary Bose-Einstein condensates. We introduce a…
We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller--Segel model of chemotaxis that includes the effect of logistic growth of the cellular population. Our analysis of localized patterns…
We extend the well-known theoretical treatment of the spontaneous symmetry breaking (SSB) in two-component systems, combining linear coupling and self-attractive nonlinearity, to a system in which the linear coupling competes with repulsive…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs)…
Among living organisms, there are species that change their patterns on their body surface during their growth process and those that maintain their patterns. Theoretically, it has been shown that large-scale species do not form distinct…
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…
This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
This paper concerns a general class of PDE-ODE reaction-diffusion systems, which features a singular fast-reaction limit towards a reaction-diffusion equation coupled to a scalar hysteresis operator. As prototypical application, we present…