Related papers: From dynamical systems with time-varying delay to …
Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…
The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the…
The framework of port-Hamiltonian (pH) systems is a powerful and broadly applicable modeling paradigm. In this paper, we extend the scope of pH systems to time-delay systems. Our definition of a delay pH system is motivated by investigating…
Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
We provide one theorem of spectral equivalence of Koopman operators of an original dynamical system and its reconstructed one through the delay-embedding technique. The theorem is proved for measure-preserving maps (e.g. dynamics on compact…
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of…
The Frimmer-Novotny model to simulate two-level systems by coupled oscillators is extended by incorporating a constant time delay in the coupling. The effects of the introduced delay on system dynamics and two-level modeling are then…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased.…
The evolution of networks of coupled chaotic maps with delayed interactions can be studied in the usual way by analyzing the evolution of the state of elements at each iteration time (the "Simulator" point of view), or it can be analyzed…
The paper deals with the global asymptotic stability of general nonlinear time-delay systems with delay-dependent impulses through the Lyapunov-Krasovskii method. We derive a unified stability criterion which can be applied to a variety of…
In multi-agent systems, heterogeneous time delays exist for all agents because of the difference in communication environments. Therefore, the consensus analysis of a system considering a homogeneous time-varying delay among all agents…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
The paper reviews positive and negative time delays in various processes of classical and quantum physics. In the beginning, we demonstrate how a time-shifted response of a system to an external perturbation appears in classical mechanics…
In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the…
In this paper, we use what we call the shift operator so that general delay dynamic equations of the form \[ x^{\Delta}(t)=a(t)x(t)+b(t)x(\delta_{-}(h,t))\delta_{-}^{\Delta}% (h,t),\ \ \ t\in\lbrack t_{0},\infty)_{\mathbb{T}}% \] can be…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order…