Studying the Stability of the Second Order Non-autonomous Hamiltonian System

It has been found that the decay in dimethylformamide and dimethylformamide-water mixtures of radical anions in five of the investigated 5-nitrofurans is governed by a second-order reaction. Only the decay of the radical anion generated from 5-nitro-2-furfural III may be described by an equation including parallel first- and second-order reactions; this behaviour is evidently caused by the relatively high stability of the corresponding dianion, this being an intermediate in the reaction path. The presence of a larger conjugated system in the substituent in position 2 results in a decrease of the unpaired electron density in the nitro group and, consequently, an increase in the stability of the corresponding radical anions.

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A contribution to the stability analysis of second-order direct-form digital filters with magnitude truncation

IEEE Transactions on Acoustics Speech and Signal Processing ◽

10.1109/tassp.1987.1165255 ◽

1987 ◽

Vol 35 (8) ◽

pp. 1207-1210 ◽

Cited By ~ 10

Author(s):

A. Lepschy ◽

G. Mian ◽

U. Viaro

Keyword(s):

Stability Analysis ◽

Digital Filters ◽

Second Order ◽

Direct Form ◽

The Stability

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Stability and resonance conditions of second-order fractional systems

Journal of Vibration and Control ◽

10.1177/1077546316654790 ◽

2016 ◽

Vol 24 (4) ◽

pp. 659-672 ◽

Cited By ~ 2

Author(s):

Elena Ivanova ◽

Xavier Moreau ◽

Rachid Malti

Keyword(s):

Second Order ◽

Damping Factor ◽

Fractional Differentiation ◽

Resonance Amplitude ◽

Fractional Systems ◽

Integral Number ◽

At Resonance ◽

Fractional System ◽

The Stability ◽

Normalized Gain

The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.

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PHASE PORTRAIT OF SECOND-ORDER DYNAMIC SYSTEMS

Applied Researches in Technics Technologies and Education ◽

10.15547/artte.2018.03.007 ◽

2018 ◽

Vol 6 (3) ◽

pp. 252-262 ◽

Cited By ~ 1

Author(s):

Kaloyan Yankov

Keyword(s):

Phase Portrait ◽

Plasma Renin ◽

Higher Order ◽

Second Order ◽

Graphical Form ◽

Time Behavior ◽

Long Time ◽

Phase Plane Method ◽

The Stability ◽

Higher Order Differential Equations

The phase portrait of the second and higher order differential equations presents in graphical form the behavior of the solution set without solving the equation. In this way, the stability of a dynamic system and its long-time behavior can be studied. The article explores the capabilities of Mathcad for analysis of systems by the phase plane method. A sequence of actions using Mathcad's operators to build phase portrait and phase trace analysis is proposed. The approach is illustrated by a model of plasma renin activity after treatment of experimental animals with nicardipine. The identified process is a differential equation of the second order. The algorithm is also applicable to systems of higher order.

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