Related papers: A Phase Model with Large Time Delayed Coupling
Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed…
We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…
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,…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
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,…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the…
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…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…
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 dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators…
We investigate the dynamics of a delay differential coupled Duffing-Van der Pol oscillator equation. Using the Lindstedt's method, we derive the in-phase mode solutions and then obtain the slow flow equations governing the stability of the…
In this paper, we study the dynamics and stability of a fundamental power system model when a time delay is imposed on the excitation of the generator. It is observed that sustained oscillations can arise in an otherwise stable power system…
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the…
We consider a model for two lasers that are mutually coupled optoelectronically by modulating the pump of one laser with the intensity deviations of the other. Signal propagation time in the optoelectronic loop causes a significant delay…