Related papers: Stochastic switching in delay-coupled oscillators
We investigate the synchronization dynamics of two coupled noise-driven FitzHugh-Nagumo systems, representing two neural populations. For certain choices of the noise intensities and coupling strength, we find cooperative stochastic…
We analyze a pair of delay-coupled FitzHugh-Nagumo oscillators exhibiting in-out intermittency as a part of the generating mechanism of extreme events. We study in detail the characteristics of in-out intermittency and identify the…
Community structure and interaction delays are common features of ensembles of network coupled oscillators, but their combined effect on the emergence of synchronization has not been studied in detail. We study the transitions between…
We theoretically study the frequency stability of an opto-mechanical radio frequency oscillator based on resonant interaction of two optical and one mechanical modes of the same optical microcavity. A generalized expression for the phase…
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…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
We study a large population of globally coupled phase oscillators subject to common white Gaussian noise and find analytically that the critical coupling strength between oscillators for synchronization transition decreases with an increase…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic…
We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated…
A lattice of three-state stochastic phase-coupled oscillators introduced by Wood it et al. exhibits a phase transition at a critical value of the coupling parameter $a$, leading to stable global oscillations (GO). On a complete graph, upon…
If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs:…
A system of ODE's is used to approximate the dynamics of two delayed coupled FitzHugh-Nagumo excitable units, and study the relevant bifurcations. It is shown that the Bautin bifurcation acts as the organizing center for the dynamics of…
We report on a novel type of instability observed in a noisy oscillator unidirectionally coupled to a pacemaker. Using a phase oscillator model, we find that, as the coupling strength is increased, the noisy oscillator lags behind the…
We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed by numerical simulations. Further detailed…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…