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We present analytical investigation of exact lag synchronization between two unidirectionally coupled identical time delay systems with two characteristic delay times, where the delay time in the coupling is different from the delay time in…
This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective…
We study two coupled systems, one playing the role of the driver system and the other one of the driven system. The driver system is a time-delayed oscillator, and the driven or response system has a negligible delay. Since the driver…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing,…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters…
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,…
It is often conjectured that quantum synchronisation and entanglement are two independent properties which two coupled quantum systems may not exhibit at the same time. However, as both these properties can be understood in terms of the…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
We experimentally demonstrate mutual synchronization of two free-running nanomechanical oscillators separated by an effective distance of 30 meters and coupled through light. Due to the finite speed of light, the large separation introduces…
We investigate the impact of a common external system, which we call a common environment, on the Oscillator Death (OD) states of a group of Stuart-Landau oscillators. The group of oscillators yield a completely symmetric OD state when…
The optoelectronic oscillator is a delay line oscillator that leverages optical fiber technology to realize the large delay required for low phase noise systems. Spurious sidemodes are an artifact of the delay line oscillator, yet…
The spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
In this article I investigate the novel synchronization behaviors of evolving pulse-coupled oscillator networks. Unlike previous models, the time-varying mechanism is inspired by neural network development, where seldom used links die out…