Related papers: Stability of diffusively coupled linear systems wi…
We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a…
We consider a large class of nonlinear diffusive systems with nonlocal coupling. By using a non-perturbative analytical approach we are able to determine the convective and absolute instabilities of all the uniform states of these systems.…
This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply 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 investigates the stability and stabilization of diffusively coupled network dynamical systems. We leverage Lyapunov methods to analyze the role of coupling in stabilizing or destabilizing network systems. We derive critical…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In this paper the linear and stationary Discrete-time systems with state variables and dynamic coefficients represented by fuzzy numbers are studied, providing some stability criteria, and characterizing the bounds of the set of solutions…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.
We establish one of the most important assumptions of the strong persistence theory for dynamical systems associated to cross diffusion systems of $m$ equations ($m\ge2$): the stable sets of semi-trivial steady cannot intersect the interior…
We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…