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We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
Second generation quantum technologies aim to outperform classical alternatives by utilizing engineered quantum systems. Maintaining the coherence required to enable any quantum advantage requires detailed knowledge and control over the…
We demonstrate that a superoscillating in time signal may be obtained as a nonlinear response on a harmonic low-frequency input. Using the realization of a superoscillating function proposed by (Huang et al. 2007 J. Opt. A: Pure Appl. Opt.…
We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the non-perturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…
An open question in mechanics is whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires engineering a mechanical nonlinearity far beyond what has been realized thus far. Here…
We consider a stochastically forced nonlinear oscillator driven by a stationary Gaussian noise that has an algebraically decaying covariance function. It is well known that such noise processes can be renormalized to converge to fractional…
Frequency entrainment of continuous-variable oscillators has to date been restrained to the weakly nonlinear regime. Here we overcome this bottleneck and extend frequency entrainment of quantum continuous-variable oscillators to arbitrary…
The paper documents the implementation of a novel phase-noise analysis module within the open-source QUCS circuit simulator environment. The underlying algorithm is based on a rigorous, unified time-domain methodology of (coupled)…
This paper is focused on the transient dynamics of an adiabatic nano-electromechanical system (NEMS), consisting of a nano-mechanical oscillator coupled to a quantum dot. By numerically solving the nonlinear stochastic differential equation…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
Nanomechanical resonators are used as high performance detectors in a variety of applications such as mass spectrometry and atomic force microscopy. Initial emphasis in nanomechanical resonant sensor research was on increasing the…
In this paper we present a theory that predicts the phase noise characteristics of self-sustained optomechanical oscillators. By treating the cavity optomechanical system as a feedback loop consisting of an optical cavity and a mechanical…
As a proof of principle, we show how a classical nonlinear Hamiltonian system can be driven resonantly over reasonably long times by appropriately shaped pulses. To keep the parameter space reasonably small, we limit ourselves to a driving…
Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of…
For noisy self-sustained oscillators, both reliability, stability of a response to a noisy driving, and coherence understood in the sense of constancy of oscillation frequency belong to the main characteristics. Though the both…
We demonstrate how noise can be turned into an advantage for optical sensing using a nonlinear cavity. The cavity is driven by a continuous wave laser into the regime of optical bistability. Due to the influence of fluctuations, the cavity…
We present a simple nonlinear resonant analog circuit which demonstrates quantization of resonating amplitudes, for a given excitation level. The system is a simple RLC resonator where C is an active capacitor whose value is related to the…
Neurons in the brain behave as non-linear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behavior to realize high density, low power neuromorphic computing will require huge…