arXiv subjects

Arkady Pikovsky

Publications and source records attributed to Arkady Pikovsky.

At least 73 records · Page 4Linked to original sources

arXiv2017

Two types of quasiperiodic partial synchrony in oscillator ensembles

We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.

nlin.CD↗

arXiv2017

Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling

We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles, and disappears in the thermodynamic limit. For all considered setups, that include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.

nlin.AO↗

arXiv2016

Interplay of coupling and common noise at the transition to synchrony in oscillator populations

We consider a population of globally coupled oscillators driven by common noise. By applying the Ott-Antonsen ansatz and by averaging over the fast oscillations, we obtain analytically tractable equations for the noisy evolution of the order parameter. While noise always tends to synchronize the oscillators, the coupling can act against synchrony if it is repulsive. For identical oscillators, the fully synchronous state remains stable for small enough repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion of the oscillators frequencies at synchrony.

nlin.AO↗

arXiv2016

Frequency locking near the gluing bifurcation: Spin-torque oscillator under periodic modulation of current

We consider entrainment by periodic force of limit cycles which are close to the homoclinic bifurcation. Taking as a physical example the nanoscale spin-torque oscillator in the LC circuit, we develop the general description of the situation in which the frequency of the stable periodic orbit in the autonomous system is highly sensitive to minor variations of the parameter, and derive explicit expressions for the strongly deformed borders of the resonance regions (Arnold tongues) in the parameter space of the problem. It turns out that proximity to homoclinic bifurcations hinders synchronization of spin-torque oscillators.

nlin.CD↗

arXiv2016

Dynamics of weakly inhomogeneous oscillator populations: Perturbation theory on top of Watanabe-Strogatz integrability

As has been shown by Watanabe and Strogatz (WS) [Phys. Rev. Lett., 70, 2391 (1993)], a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system for any size: its dynamics reduces to equations for several collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: due to a distribution of natural frequencies and of forcing terms, and due to small white noise. We demonstrate, that in both cases the complex mean field for which the dynamical equations are written, is close up to the leading order in the perturbation to the Kuramoto order parameter. This supports validity of the dynamical reduction suggested by Ott and Antonsen [Chaos, 18, 037113 (2008)] for weakly inhomogeneous populations.

nlin.CD↗

arXiv2016

Star-type oscillatory networks with generic Kuramoto-type coupling: a model for "Japanese drums synchrony"

We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, that gives full an- alytical description of states, rotating with constant frequency. For nonidentical oscillators, such states can be obtained by virtue of the self-consistent approach in a parametric form. In this case stability analysis cannot be performed, however with the help of direct numerical simulations we show which solutions are stable and which not. We consider this system as a model for a drum orchestra, where we assume that the drummers follow the signal of the leader without listening to each other and the coupling parameters are determined by a geometrical organization of the orchestra.

nlin.AO↗

arXiv2015

Dynamics of globally coupled oscillators: progress and perspectives

In this paper we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches.

nlin.AO↗

arXiv2015

Maximizing coherence of oscillations by external locking

We study how the coherence of noisy oscillations can be optimally enhanced by external locking. Basing on the condition of minimizing the phase diffusion constant, we find the optimal forcing explicitly in the limits of small and large noise, in dependence of phase sensitivity of the oscillator. We show that the form of the optimal force bifurcates with the noise intensity. In the limit of small noise, the results are compared with purely deterministic conditions of optimal locking.

nlin.CD↗

arXiv2015

Inter-community resonances in multifrequency ensembles of coupled oscillators

We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to resonance 2:1 is considered in detail. We derive uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross-coupling between the frequency scales can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross-coupling is accompanied by a huge multiplicity of distinct synchronous solutions what is directly related to a multi-branch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy a phase-locking and lead to chaos of mean fields.

nlin.AO↗

arXiv2015

Partial synchronization phenomena in networks of identical oscillators with non-linear coupling

We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e. in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, and different network sizes, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.

nlin.AO↗

arXiv2015

Comment on "Asymptotic Phase for Stochastic Oscillators"

Definition of the phase of oscillations is straightforward for deterministic periodic processes but nontrivial for stochastic ones. Recently, Thomas and Lindner in [Phys. Rev. Lett., v. 113, 254101 (2014)] suggested to use the argument of the complex eigenfunction of the backward density evolution operator with the smallest real part of the eigenvalue, as an asymptotic phase of stochastic oscillations. Here I show that this definition does not generally provide a correct asymptotic phase.

nlin.CD↗

arXiv2014

Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings

We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spins with ferromagnetic and nematic coupling. We demonstrate the inequivalence by mapping the microcanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams.

cond-mat.stat-mech↗

arXiv2014

Mixed mode synchronization and network bursting of neurons with post-inhibitory rebound

This study is focused on the mechanisms of rhythmogenesis and robustness of anti-phase bursting in half-center-oscillators (HCOs) consisting of two reciprocally inhibitory coupled neurons. There is a growing body of experimental evidence that a HCO is a universal building block for larger neural networks, including central pattern generators (CPGs) controlling a variety of locomotion behaviors in spineless animals and mammals. It remains unclear how CPGs achieve the level of robustness and stability observed in nature. There has been a vastly growing consensus in the community of neurophysiologists and computational researchers that some basic structural and functional elements are likely shared by CPGs of both invertebrate and vertebrate animals. In this study we consider several configurations of HCOs including coupled endogenous bursters, tonic spiking, and quiescent neurons, that become network bursters only when coupled by fast inhibitory synapses through the mechanism of post-inhibitory-rebound (PIR). The goal is better understanding the PIR mechanism as a key component for robust anti-phase bursting in generic HCOs

nlin.CD↗

arXiv2014

Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling

We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony where possible scenarios include: simple supercritical transition (similar to classical Kuramoto model), subcritical transition with large area of bistability of incoherent and synchronous solutions, and also appearance of symmetric two-cluster solution which can coexist with regular synchronous state. Remarkably, we show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastable asynchronous solution.

nlin.AO↗

arXiv2014

Nonreciprocal wave scattering on nonlinear string-coupled oscillators

We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: the same wave is transmitted differently in two directions. Periodic regimes of scattering are analysed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a "chaotic diode", where transmission is periodic in one direction and chaotic in the opposite one, is reported.

nlin.CD↗

arXiv2014

Effective phase connectivity from observations

We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pair-wise one. Our technique reveals effective phase connectivity which is generally not equivalent to structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.

nlin.CD↗

arXiv2014

Synchronization of oscillators in a Kuramoto-type model with generic coupling

We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of oscillators to the mean field and to different forces from the mean field on oscillators. We present the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. As an example we consider spatially spreaded oscillators, for which the coupling properties are determined by finite velocity of signal propagation.

nlin.CD↗

arXiv2014

Synchronization transitions in globally coupled rotors in presence of noise and inertia: Exact results

We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes previously studied Sakaguchi-Kuramoto, Hamiltonian and Brownian mean-field, and Tanaka-Lichtenberg-Oishi and Acebrón-Bonilla-Spigler models. We derive an exact solution of the self-consistent equations for the order parameter in the stationary state, valid for arbitrary parameters in the dynamics, and demonstrate nontrivial phase transitions to synchrony that include reentrant synchronous regimes.

nlin.CD↗