Stability and resonance conditions of second-order fractional systems

2016 ◽  
Vol 24 (4) ◽  
pp. 659-672 ◽  
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.

scholarly journals Stability Analysis of Distributed Order Fractional Chen System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
H. Aminikhah ◽  
A. Refahi Sheikhani ◽  
H. Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Numerical Solutions ◽  
Necessary Conditions ◽  
Chen System ◽  
Fractional Systems ◽  
Sufficient And Necessary Conditions ◽  
Fractional System ◽  
The Stability ◽  
Conditions Of Stability ◽  
Distributed Order

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.

Stability of radical anions derived from substituted 5-nitrofurans investigated by ESR spectroscopy

1985 ◽  
Vol 50 (7) ◽  
pp. 1594-1601 ◽  
Author(s):  
Jiří Klíma ◽  
Larisa Baumane ◽  
Janis Stradinš ◽  
Jiří Volke ◽  
Romualds Gavars
Keyword(s):  
Radical Anion ◽  
High Stability ◽  
Esr Spectroscopy ◽  
Reaction Path ◽  
Order Reaction ◽  
Second Order ◽  
Radical Anions ◽  
Second Order Reaction ◽  
Unpaired Electron Density ◽  
The Stability

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.

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

scholarly journals PHASE PORTRAIT OF SECOND-ORDER DYNAMIC SYSTEMS

2018 ◽  
Vol 6 (3) ◽  
pp. 252-262 ◽  
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.

Stability of Forced Oscillations With Nonlinear Second-Order Terms

1959 ◽  
Vol 26 (4) ◽  
pp. 499-502
Author(s):  
Chi-Neng Shen
Keyword(s):  
Continued Fraction ◽  
Variational Equation ◽  
Second Order ◽  
Iteration Procedure ◽  
Forced Oscillations ◽  
The Stability ◽  
Boundary Of Stability

Abstract A solution is obtained for forced oscillations with nonlinear second-order terms. The stability of this solution is given by its variational equation. The boundary of stability is analyzed by both the perturbation and continued fraction methods. The amplitude of osclllation with damping terms is also determined by the iteration procedure.

Evaluating second-order effects in rigid wall-flexible roof diaphragm buildings

2020 ◽  
Vol 36 (4) ◽  
pp. 1864-1885
Author(s):  
John Lawson ◽  
Maria Koliou
Keyword(s):  
Rigid Wall ◽  
The United States ◽  
Second Order ◽  
Order Effects ◽  
Building Stock ◽  
Stability Coefficient ◽  
Multistory Buildings ◽  
Flexible Diaphragm ◽  
Second Order Effects ◽  
The Stability

When evaluating seismically induced second-order effects in buildings, engineers and researchers are most familiar with these concerns in the context of multistory buildings with rigid diaphragms. However, similar concerns are valid for short single-story concrete or masonry-walled buildings with larger flexible diaphragms, which is a significant portion of the building stock in the United States. These rigid wall-flexible diaphragm (RWFD) buildings may have significant diaphragm drifts causing induced second-order effects. The stability coefficient currently found in ASCE 7 has traditionally been used by practitioners to evaluate the relative risk of P-delta instability in multistory buildings, but this indicator can be adapted for use in RWFD buildings. Using numerical studies following the Federal Emergency Management Agency (FEMA) P-695 collapse assessment methodology to evaluate the risk of collapse for a set of RWFD archetype buildings, a modified stability coefficient for RWFD buildings is found to capture the trend toward P-delta collapse and can act as a reasonable indicator without the need for heavy computational efforts.

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