Selective Determination of Floquet Quantities for the Efficient Assessment of Limit Cycle Stability and Oscillator Noise

Traversa, Fabio L.; Bonani, Fabrizio

doi:10.1109/tcad.2012.2214480

Cited by 15 publications

(4 citation statements)

References 20 publications

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“…In most of the cases, the computation is perfomed in time domain [36][37][38][39]. However, efficient algorithms for the frequemcy domain evaluation, based on the harmonic balance technique, are proposed in [34,38,[40][41][42][43].…”

Section: A Floquet Theory Basicsmentioning

confidence: 99%

Noise in oscillators: a review of state space decomposition approaches

et al. 2014

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We review the state space decomposition techniques for the assessment of the noise properties of autonomous oscillators, a topic of great practical and theoretical importance for many applications in many different fields, from electronics, to optics, to biology. After presenting a rigorous definition of phase, given in terms of the autonomous system isochrons, we provide a generalized projection technique that allows to decompose the oscillator fluctuations in terms of phase and amplitude noise, pointing out that the very definition of phase (and orbital) deviations depends of the base chosen to define the aforementioned projection. After reviewing the most advanced theories for phase noise, based on the use of the Floquet basis and of the reduction of the projected model by neglecting the orbital fluctuations, we discuss the intricacies of the phase reduction process pointing out the presence of possible variations of the noisy oscillator frequency due to amplitude-related effects.

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Section: A Floquet Theory Basicsmentioning

confidence: 99%

Noise in oscillators: a review of state space decomposition approaches

et al. 2014

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“…The explicit expression for such a generalized eigenvalue problem depends on the features of the memory kernel K(t, τ ). Since all the terms of ( 6) are T -periodic, a viable solution strategy is the use of frequency-domain approaches such as the Harmonic Balance (HB) technique [21][22][23][24], here summarized in Appendix C. Frequency transformation of (6) yields…”

Section: Floquet Exponents Computationmentioning

confidence: 99%

Application of Floquet theory to dynamical systems with memory

Traversa

Ventra

Cappelluti

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We extend the recently developed generalized Floquet theory [Phys. Rev. Lett. 110, 170602 (2013)] to systems with infinite memory. In particular, we show that a lower asymptotic bound exists for the Floquet exponents associated to such cases. As examples, we analyze the cases of an ideal 1D system, a Brownian particle, and a circuit resonator with an ideal transmission line. All these examples show the usefulness of this new approach to the study of dynamical systems with memory, which are ubiquitous in science and technology.

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“…For second order systems, Floquet basis and co-basis can be computed using the formulas given in [84], while for higher order systems, numerical methods are needed [113][114][115]. Since the goal of this work is to illustrate fundamental principles avoiding technicalities as much as possible, we shall consider the weakly nonlinear version of (30) (i.e., we assume 𝛼 1).…”

Section: Examplementioning

confidence: 99%

Coupled oscillator networks for von Neumann and non von Neumann computing

Bonnin¹,

Traversa²,

Bonani³

2020

Preprint

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The frenetic growth of the need for computation performance and efficiency, along with the intrinsic limitations of the current main solutions, is pushing the scientific community towards unconventional, and sometimes even exotic, alternatives to the standard computing architectures. In this work we provide a panorama of the most relevant alternatives, both according and not the von Neumann architecture, highlighting which of the classical challenges, such as energy efficiency and/or computational complexity, they are trying to tackle. We focus on the alternatives based on networks of weakly coupled oscillators. This unconventional approach, already introduced by Goto and Von Neumann in the 50s, is recently regaining interest with potential applications to both von Neumann and non von Neumann type of computing. In this contribution, we present a general framework based on the phase equation we derive from the description of nonlinear weakly coupled oscillators especially useful for computing applications. We then use this formalism to design and prove the working principle and stability assessment of Boolean gates such as NOT and MAJORITY, that can be potentially employed as building blocks for both von Neumann and non-von Neumann architectures.

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Selective Determination of Floquet Quantities for the Efficient Assessment of Limit Cycle Stability and Oscillator Noise

Cited by 15 publications

References 20 publications

Noise in oscillators: a review of state space decomposition approaches

Noise in oscillators: a review of state space decomposition approaches

Application of Floquet theory to dynamical systems with memory

Coupled oscillator networks for von Neumann and non von Neumann computing

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