Related papers: Leibniz Dynamics with Time Delay
We study the reduction of non-autonomous regular Lagrangian systems by symmetries, which are generated by vector fields associated with connections in the configuration bundle of the system $Q\times\real\to\real$. These kind of symmetries…
We study the occurence of delay mechanisms other than periodic orbits in systems with time dependent potentials that exhibit chaotic scattering. By using as model system two harmonically oscillating disks on a plane, we have found the…
Significant variations of delays among connecting neurons cause an inevitable disadvantage of asynchronous brain dynamics compared to synchronous deep learning. However, this study demonstrates that this disadvantage can be converted into a…
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay…
We design a Linear Chain Trick (LCT)-algorithm for dynamical systems with distributed time delay where the time histories contain temporal oscillations. The methodology is illustrated by means of an example in population dynamics.
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of…
In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively…
This paper considers $L_2$ and BIBO stability and stabilization issues for systems with time-varying delays which can be of retarded or neutral type. An important role is played by a nominal system with fixed delays which are close to the…
Many real-analytic flows, e.g. in chemical kinetics, share a multiple time scale spectral structure. The trajectories of the corresponding dynamical systems are observed to bundle near so-called slow invariant manifolds (SIMs), which are…
Wigner-Smith (WS) time delay concepts have been used extensively in quantum mechanics to characterize delays experienced by particles interacting with a potential well. This paper formally extends WS time delay theory to Maxwell's equations…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled…
We propose and study a system whose dynamics are governed by predictions of its future states. General formalism and concrete examples are presented. We find that the dynamical characteristics depend on both how to shape predictions as well…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
A previously published algorithm for trajectory tracking control of tethered wings, i.e. kites, is updated in light of recent experimental evidence. The algorithm is, furthermore, analyzed in the framework of delay differential equations.…
The concepts of Wigner time delay and Wigner-Smith matrix allow to characterize temporal aspects of a quantum scattering process. The article reviews the statistical properties of the Wigner time delay for disordered systems; the case of…
Feedback control plays a central role in active matter, yet it is inevitably accompanied by noise and finite perception--action delays. This Perspective reviews recent advances on active systems with delayed interactions, showing how time…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…