Related papers: Hyperbolicity of linear partial differential equat…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes.
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
Delayed feedback laser dynamics is described by means of Lang-Kobayashi equation model. Since a lot of initial states asymptotically approach to periodic attractor in the phase space, only periodic steady-state regimes have been studied…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
We design the controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…
We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting and neutral manifolds of…
In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…
Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…
We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.