Substantial evidence indicates that the brain uses principles of non-linear dynamics in neural processes, providing inspiration for computing with nanoelectronic devices. However, training neural networks composed of dynamical nanodevices requires finely controlling and tuning their coupled oscillations. In this work, we show that the outstanding tunability of spintronic nano-oscillators can so...

A method of proving the existence of breathers in lattices of two-dimensional weakly coupled Hamiltonian oscillators is presented. This method has the advantage that provides a first approximation of the initial conditions of the breather solution together with its linear stability. Since the proof relies on the use of action-angle variables, we also present a method to perform the calculations...

We consider two and three phase-oscillators as in the Kuramoto model of coupled oscillators, replacing the sine wave interaction with a sawtooth wave. We show that for the case of non-uniform input-symmetric coupling strengths, the non-smooth, piecewise-linear dynamics synchronizes when the coupling strengths are large enough to overcome the differences in the natural frequencies of the oscilla...

We study two-cluster solutions of an ensemble of generic limit-cycle oscillators in the vicinity of a Hopf bifurcation, i.e., Stuart-Landau oscillators, with a nonlinear global coupling. This coupling leads to conserved mean-field oscillations acting back on the individual oscillators as a forcing. A reduction to two effective equations makes a linear stability analysis of the cluster solutions...

the prediction of the joint angle position, especially during tremor bursts, can be useful for detecting, tracking, and forecasting tremors. thus, this research proposes a new model for predicting the wrist joint position during rhythmic bursts and inter‑burst intervals. since a tremor is an approximately rhythmic and roughly sinusoidal movement, neural oscillators have been selected to underli...

We consider a network of deterministic non-linear oscillators with nonidentical parameters. Interactions between the different oscillators are linear, but the coupling coefficients for each interaction may differ. We consider the case where coupling coefficients are sufficiently large, so that the different oscillators will have their state variables strongly tied together and variables of the ...

The D-dimensional (β, β ′)-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a (D + 1)-dimensional quan-tized spacetime. In the D = 3 and β = 0 case, the latter reproduces Snyder algebra. The deformed Poincaré transformations leaving the algebra invariant are identified. It is shown that there exists a nonzero minimal uncertainty in posi...

Mutual synchronization is a ubiquitous phenomenon that exists in various natural systems. The individual participants in this process can be modeled as oscillators, which interact by discrete pulses. In this paper, we analyze the synchronization condition of twoand multi-oscillators system, and propose a linear pulse-coupled oscillators model. We prove that the proposed model can achieve synchr...

We propose a multiscale method to study nanotube-based resonant oscillators. In the multiscale model, nanotubes are modeled via molecular dynamics, while the metal paddle is modeled as a rigid body. The molecular and continuum models are attached to each other through the interfaces on which carbon atoms are located. We employ the concepts of “virtual” atoms and bonds to effectively couple the ...

We study neuro-computational properties of non-linear oscillatory systems. Since we use the canonical phase models approach, our results do not depend on the physical nature of each oscillator or the detailed form of mathematical equations that describe its dynamics. In particular, we show that anything that can oscillate can also compute, the only problem is how to couple the oscillators. We a...