相关论文: Existence and instability of steady states for a t…
The steady state of a Brownian particle diffusing in an arbitrary potential under the stochastic resetting mechanism has been studied. We show that there are different classes of nonequilibrium steady states depending on the nature of the…
Solving problems related to open quantum systems has attracted many interests. Here, we propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
The paper discusses a simple method of using the parametric continuation method to designate complex diagrams of steady states. The main advantage of the discussed approach is the fact that it does not require the installation of huge…
In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of globally exponentially stable…
Sufficient conditions for the wave instability in general three-component reaction-diffusion systems are derived. These conditions are expressed in terms of the Jacobian matrix of the uniform steady state of the system, and enable us to…
There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…
Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
We present a general non-perturbative method to determine the exact steady state of open quantum systems under perturbation. The method works for systems with a unique steady state and the perturbation may be time-independent or periodic,…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
We establish the existence of a stable foliation in the vicinity of a traveling front solution for systems of reaction diffusion equations in one space dimension that arise in the study of chemical reactions models and solid fuel…
It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first analyze a three-species system with boundary equilibria in…