Effect of delayed feedback on the dynamics of a scalar map via a frequency-domain approach

Gentile, Franco S.; Bel, Andrea; D’Amico, María Belén; Moiola, Jorge L.

doi:10.1063/1.3595707

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Cited by 5 publications

(3 citation statements)

References 18 publications

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“…Within the context of self-excited systems, Lur'e systems under various assumptions are considered in [4,5,6,7,8,9,1,10,11,12]. Self-oscillating discrete-time systems are considered in [13,14].…”

Section: Introductionmentioning

confidence: 99%

Self-Excited Dynamics of Discrete-Time Lur'e Systems

Paredes,

Islam,

Kouba

et al. 2021

Preprint

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Section: Introductionmentioning

confidence: 99%

Self-Excited Dynamics of Discrete-Time Lur'e Systems

Paredes,

Islam,

Kouba

et al. 2021

Preprint

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“…Application to thermoacoustic oscillation in combustors is considered in [25]. Self-oscillating discrete-time systems are considered in [26]- [29].…”

Section: Introductionmentioning

confidence: 99%

A Time-Delayed Lur’e Model with Biased Self-Excited Oscillations

Paredes

Islam

Bernstein

2020

2020 American Control Conference (ACC)

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Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluid-structure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur'e model that exhibits biased selfexcited oscillations under constant inputs. The model involves asymptotically stable linear dynamics, time delay, a washout filter, and a saturation nonlinearity. For all sufficiently large scalings of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an oscillatory response. A bias-generation mechanism is used to specify the mean of the oscillation. The main contribution of the paper is a detailed analysis of a discrete-time version of this model.

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“…The equivalent input-output representation makes it possible to reduce the dimension of the states, facilitating the calculations. 42 …”

Section: Examplesmentioning

confidence: 99%

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

D’Amico

Calandrini

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

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Effect of delayed feedback on the dynamics of a scalar map via a frequency-domain approach

Cited by 5 publications

References 18 publications

Self-Excited Dynamics of Discrete-Time Lur'e Systems

Self-Excited Dynamics of Discrete-Time Lur'e Systems

A Time-Delayed Lur’e Model with Biased Self-Excited Oscillations

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

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