Related papers: Chaos in time delay systems, an educational review
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
We develop an extension of the fast method of angles for hyperbolicity verification in chaotic systems with an arbitrary number of time-delay feedback loops. The adopted method is based on the theory of covariant Lyapunov vectors and…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
in the last decade, studies of chaotic system are more often used for classical choatic system than for quantum chaotic system, there are many ways of observing the chaotic system such us analyzing the frequency with Fourier transform or…
Chaos degree defined through two complexities in information dynamics is applied to some deterministic dynamical models. It is shown that this degree well describes the chaostic feature of the models.
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
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…
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay…
In public railway systems, minor disruptions can trigger cascading events that lead to delays in the entire system. Typically, delays originate and propagate because the equipment is blocking ways, operational units are unavailable, or at…
In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…
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…
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…
We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time…
The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin…