Related papers: Dynamical behaviours in time-delay systems with de…
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…
Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a…
The phenomenon of amplitude death has been explored using a variety of different coupling strategies in the last two decades. In most of the work, the basic coupling arrangement is considered to be static over time, although many realistic…
We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's…
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…
Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This…
We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics,…
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…
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article…
We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard…
We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of…
We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In…
We find chimera states with respect to amplitude dynamics in a network of Stuart-Landau oscillators. These partially coherent and partially incoherent spatio-temporal patterns appear due to the interplay of nonlocal network topology and…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of…