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Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…
In this letter we consider a prototype model which is described as an autonomous continuous time delayed differential equation with just one variable. The chaos has been investigated with variable delay time and the synchronization…
Stiff and chaotic differential equations are challenging for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution…
We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate $2…
The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent…
This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
Hyperchaos is a qualitatively stronger form of chaos, in which several degrees of freedom contribute simultaneously to exponential divergence of small changes. A hyperchaotic dynamical system is therefore even more unpredictable than a…
This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the…
Systems with delayed feedback can possess chaotic attractors with extremely high dimension, even if only a few physical degrees of freedom are involved. We propose a state space reconstruction from time series data of a scalar observable,…
A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering.…
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant delays. The methodology suggested provides algorithms of…
General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations which affect essentially all degrees of freedom we find a doubly exponential decay with the rate…
A method to synchronize two chaotic systems with anticipation or lag, coupled in the drive response mode, is proposed. The coupling involves variable delay with three time scales. The method has the advantage that synchronization is…