Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators

We consider collective dynamics in the ensemble of serially connected spin-torque oscillators governed by the Landau-Lifshitz-Gilbert-Slonczewski magnetization equation. Proximity to homoclinicity hampers synchronization of spin-torque oscillators: when the synchronous ensemble experiences the homoclinic bifurcation, the Floquet multiplier, responsible for the temporal evolution of small deviations from the ensemble mean, diverges. Depending on the configuration of the contour, sufficiently strong common noise, exemplified by stochastic oscillations of the current through the circuit, may suppress precession of the magnetic field for all oscillators. We derive the explicit expression for the threshold amplitude of noise, enabling this suppression.Comment: 12 pages, 13 figure

Collective Phase Sensitivity

The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase sensitivity is derived from the microscopic phase sensitivity of the constituent oscillators by a two-step phase reduction. We apply this result to quantify the stability of the macroscopic common-noise induced synchronization of two uncoupled populations of oscillators undergoing coherent collective oscillations.Comment: 6 pages, 3 figure

Dynamics of Limit Cycle Oscillator Subject to General Noise

The phase description is a powerful tool for analyzing noisy limit cycle oscillators. The method, however, has found only limited applications so far, because the present theory is applicable only to the Gaussian noise while noise in the real world often has non-Gaussian statistics. Here, we provide the phase reduction for limit cycle oscillators subject to general, colored and non-Gaussian, noise including heavy-tailed noise. We derive quantifiers like mean frequency, diffusion constant, and the Lyapunov exponent to confirm consistency of the result. Applying our results, we additionally study a resonance between the phase and noise.Comment: main paper: 4 pages, 2 figure; auxiliary material: 5-7 pages of the document, 1 figur

Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always results from arbitrary initial conditions, irrespective of the details of the oscillators.Comment: 6 pages, 2 figure

Stochastic stability and moment Lyapunov exponent for co-dimension two bifurcation system with a bounded noise

In this paper, the pth moment Lyapunov exponent of a co-dimension two bifurcation system that is parametrically excited by a real noise is investigated. By a linear stochastic transformation, the eigenvalue problem of moment Lyapunov exponent is obtained. Then through perturbation method, we deduce the joint probability density function of the phase processes and its eigenvalue problem, which is solved by a Fourier cosine series expansion. Thus, an infinite matrix yields and whose leading eigenvalue is the second order of the asymptotic expansion of the moment Lyapunov exponent. Because of the complexity of elements in matrix A, the eigenvalues of the low order sub-matrices of A are obtained by the truncation of n and the convergence of the eigenvalue sequence is numerically illustrated. Finally, the effects of the system and noise parameters on the moment Lyapunov exponent are discussed

Experimental synchronization of circuit oscillations induced by common telegraph noise

Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous formulation [K. Nagai et al., Phys. Rev. E 71, 036217 (2005)], dynamics of the circuit is described as random-phase mappings between two limit cycles. Lyapunov exponents characterizing the degree of synchronization are estimated from experimentally determined phase maps and compared with linear damping rates of phase differences measured directly. Noisy on-off intermittency of the phase difference as predicted by the theory is also confirmed experimentally

MOMENT LYAPUNOV EXPONENTS AND STOCHASTIC STABILITY OF A THIN-WALLED BEAM SUBJECTED TO AXIAL LOADS AND END MOMENTS

In this paper, the Lyapunov exponent and moment Lyapunov exponents of two degrees-of-freedom linear systems subjected to white noise parametric excitation are investigated. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining both the almost-sure and the moment stability of a stochastic dynamic system. As an example, we study the almost-sure and moment stability of a thin-walled beam subjected to stochastic axial load and stochastically fluctuating end moments.  The validity of the approximate results for moment Lyapunov exponents is checked by numerical Monte Carlo simulation method for this stochastic system