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Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
The two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of…
Advances in optical measurements enable precise tracking of cavity polariton wave-packets across broad spatial and temporal ranges, but how dephasing reshapes their real-space dynamics over multiple time scales remains unclear. Here we…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single…
The dust-acoustic waves and their stability in the permeating dusty plasma with the Maxwellian velocity distribution are investigated. We derive the dust-acoustic wave frequency and instability growth rate in two limiting physical cases…
We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than…
A simplified model of the tumor angiogenesis can be described by a Keller-Segel equation \cite{FrTe,Le,Pe}. The stability of traveling waves for the one dimensional system has recently been known by \cite{JinLiWa,LiWa}. In this paper we…
Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp $L^p$ estimates on the linearized solution operator about a multidimensional planar periodic…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
Paints and coatings often feature interfacial defects due to disturbances during the deposition process which, if they persist until solidification, worsen the product quality. In this article, we investigate the stability of a thin liquid…
The problem of the stability of a nonlinear thermomagnetic wave with respect to small thermal and electromagnetic perturbations in hard superconductors was studied. It is shown that spatially bounded solutions may correspond only to the…
We investigate a driven, one-dimensional system of colloidal particles in a periodically currogated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory,…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy)…
The far-from-equilibrium dynamics of two crystalline two-dimensional monolayers driven past each other is studied using Brownian dynamics simulations. While at very high and low driving rates the layers slide past one another retaining…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
Spontaneous pattern formation in a variety of spatially extended nonlinear system always occurs through a modulation instability: homogeneous state of the system becomes unstable with respect to growing modulation modes. Therefore, the…