Neural oscillators with a ladder-like structure is one of the central pattern generator (CPG) model that is used to simulate rhythmic movements in living organisms. However, it is not easy to realize rhythmical cycles by tuning many parameters of neural oscillators. In this study, we propose an automatic tuning method. We derive the tuning rules for both the time constants and the coefficients ...

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 synch...

We combine here two well-known and established concepts: microelectromechanical systems (MEMS) and neurocomputing. First, we consider MEMS oscillators having low amplitude activity and we derive a simple mathematical model that describes nonlinear phase-locking dynamics in them. Then, we investigate a theoretical possibility of using MEMS oscillators to build an oscillatory neurocomputer having...

A laser model is formulated in terms of quantum harmonic oscillators. Emitters the low lasing states are usual oscillators, and emitters upper inverted Diffusion coefficients, consistent with necessary for solving nonlinear equations analytically, found. Photon number fluctuations mode population calculated. Collective Rabi splitting peaks predicted intensity fluctuation spectra superradiant la...

AppIied Mathematics Letters ~w.el~vier.ni/~ocate/~l Abstract-we contribute to the method of trigonometric series for solving differential equations of certain nonlinear oscillators.

We study an infinite assembly of integrate and fire oscillators with global coupling. Numerical simulations reveal that the time required for the mutual synchrony of all the oscillators exhibits singular behavior as a function of the interaction strength. The origin of this anomalous synchronization is elucidated by a theoretical analysis. Synchronization is one of the most fascinating nonlinea...

We generalize our recent approach to the reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from a multivariate time series, we first reconstruct genuine phases and then obtain the coupling functions in terms of these phases. Partial norms of these couplin...

Bispectral analysis, a technique based on high-order statistics, is extended to encompass time dependence for the case of coupled nonlinear oscillators. It is applicable to univariate as well as to multivariate data obtained, respectively, from one or more of the oscillators. It is demonstrated for a generic model of interacting systems whose basic units are the Poincaré oscillators. Their freq...

A mild, nonlinear, time-delayed feedback signal was applied to two heterogeneous oscillators in order to synchronize their frequencies with an arbitrary and controllable phase difference. The feedback was designed using phase models constructed from experimental measurements of the intrinsic dynamical properties of the oscillators. The feedback signal produced an interaction function that corre...

An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of t...