Related papers: Stability of fronts in the diffusive Rosenzweig-Ma…
Motivated by radiation hydrodynamics, we analyse a 2x2 system consisting of a one-dimensional viscous conservation law with strictly convex flux -- the viscous Burgers' equation being a paradigmatic example -- coupled with an elliptic…
A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
We analyze the dynamics of pattern forming fronts which propagate into an unstable state, and whose dynamics is of the pulled type, so that their asymptotic speed is equal to the linear spreading speed v^*. We discuss a method that allows…
In this paper, we study the existence and stability of random transition waves for time heterogeneous Fisher-KPP Equations with nonlocal diffusion. More specifically, we consider general time heterogeneities both for the nonlocal diffusion…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: $(1)$ prey movement follows a nonlinear diffusion, $(2)$ preys have a refuge zone (sometimes called "protection zone") where predators cannot…
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…
In the current series of two papers, we study the long time behavior of the following random Fisher-KPP equation $$ u_t =u_{xx}+a(\theta_t\omega)u(1-u),\quad x\in\R, \eqno(1) $$ where $\omega\in\Omega$, $(\Omega, \mathcal{F},\mathbb{P})$ is…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
We here discretize a predator-prey model by standard Euler forward method and non-standard finite difference method and then compare their dynamic properties with the corresponding continuous-time model. We show that NSFD model preserves…
We consider the damped hyperbolic equation in one space dimension $\epsilon u_{tt} + u_t = u_{xx} + F(u)$, where $\epsilon$ is a positive, not necessarily small parameter. We assume that $F(0)=F(1)=0$ and that $F$ is concave on the interval…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A <-> A$ on the lattice when only a particle is allowed per site.…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex perturbations. This extends the results of…
A cubic discrete coupled logistic equation is proposed to model the predator-prey problem. The coupling depends on the population size of both species and on a positive constant $\lambda$, which could depend on the prey reproduction rate…
The Rosenbluth-Fokker-Planck (RFP) equation describes Coulomb collisional dynamics within and across species in plasmas. It belongs to the broader class of anisotropic-diffusion-advection equations, whose numerical approximation is…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…