On the stability parameters of periodic solutions

1976 ◽  
Vol 43 (2) ◽  
pp. 449-458 ◽  
Author(s):  
V. V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Stability Parameters ◽  
The Stability

Experimentally Determined Stability Parameters of a Subsonic Cascade Oscillating Near Stall

1978 ◽  
Vol 100 (1) ◽  
pp. 111-120 ◽  
Author(s):  
F. O. Carta ◽  
A. O. St. Hilaire
Keyword(s):  
Phase Angle ◽  
Incidence Angle ◽  
Minor Effect ◽  
Significant Finding ◽  
Force Coefficient ◽  
Stability Parameters ◽  
Free System ◽  
Pressure Transducers ◽  
Moment Coefficient ◽  
The Stability

Tests were performed on a linear cascade of airfoils oscillating in pitch about their midchords at frequencies up to 17 cps, at free-stream velocities up to 200 ft/s, and at interblade phase angles of 0 deg and 45 deg, under conditions of high aerodynamic loading. The measured data included unsteady time histories from chordwise pressure transducers and from chordwise hot films. Unsteady normal force coefficient, moment coefficient, and aerodynamic work per cycle of oscillation were obtained from integrals of the pressure data, and indications of the nature and extent of the separation phenomenon were obtained from an analysis of the hot-film response data. The most significant finding of this investigation is that a change in interblade phase angle from 0 deg to 45 deg radically alters the character of the unsteady blade loading (which governs its motion in a free system) from stable to unstable. Furthermore, the stability or instability is governed primarily by the phase angle of the pressure distribution (relative to the blade motion) over the forward 10–15 percent of the blade chord. Reduced frequency and mean incidence angle changes were found to have a relatively minor effect on stability for the range of parameters tested.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

2009 ◽  
Author(s):  
W. T. van Horssen ◽  
O. V. Pischanskyy ◽  
J. L. A. Dubbeldam
Keyword(s):  
Periodic Solutions ◽  
Forced Vibrations ◽  
Time Varying ◽  
Mass System ◽  
Single Degree Of Freedom ◽  
Stability Properties ◽  
Single Degree ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Varying Mass

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

Hopf Bifurcation Induced by Delay Effect in a Diffusive Tumor-Immune System

2018 ◽  
Vol 28 (11) ◽  
pp. 1850136 ◽  
Author(s):  
Ben Niu ◽  
Yuxiao Guo ◽  
Yanfei Du
Keyword(s):  
Immune System ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Center Manifold ◽  
Immune Cell ◽  
Tumor Treatment ◽  
Delay Effect ◽  
Stable Periodic ◽  
The Stability ◽  
Bifurcation And Stability

Tumor-immune interaction plays an important role in the tumor treatment. We analyze the stability of steady states in a diffusive tumor-immune model with response and proliferation delay [Formula: see text] of immune system where the immune cell has a probability [Formula: see text] in killing tumor cells. We find increasing time delay [Formula: see text] destabilizes the positive steady state and induces Hopf bifurcations. The criticality of Hopf bifurcation is investigated by deriving normal forms on the center manifold, then the direction of bifurcation and stability of bifurcating periodic solutions are determined. Using a group of parameters to simulate the system, stable periodic solutions are found near the Hopf bifurcation. The effect of killing probability [Formula: see text] on Hopf bifurcation values is also discussed.

scholarly journals Rise and Decay of the COVID-19 Epidemics in the USA and the State of New York in the First Half of 2020: A Nonlinear Physics Perspective Yielding Novel Insights

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Till D. Frank
Keyword(s):  
New York ◽  
Human Life ◽  
Compartment Model ◽  
The State ◽  
Stability Parameters ◽  
Intervention Measures ◽  
Infection Dynamics ◽  
The Usa ◽  
Three Stages ◽  
The Stability

As of December 2020, since the beginning of the year 2020, the COVID-19 pandemic has claimed worldwide more than 1 million lives and has changed human life in unprecedented ways. Despite the fact that the pandemic is far from over, several countries managed at least temporarily to make their first-wave COVID-19 epidemics to subside to relatively low levels. Combining an epidemiological compartment model and a stability analysis as used in nonlinear physics and synergetics, it is shown how the first-wave epidemics in the state of New York and nationwide in the USA developed through three stages during the first half of the year 2020. These three stages are the outbreak stage, the linear stage, and the subsiding stage. Evidence is given that the COVID-19 outbreaks in these two regions were due to instabilities of the COVID-19 free states of the corresponding infection dynamical systems. It is shown that from stage 1 to stage 3, these instabilities were removed, presumably due to intervention measures, in the sense that the COVID-19 free states were stabilized in the months of May and June in both regions. In this context, stability parameters and key directions are identified that characterize the infection dynamics in the outbreak and subsiding stages. Importantly, it is shown that the directions in combination with the sign-switching of the stability parameters can explain the observed rise and decay of the epidemics in the state of New York and the USA. The nonlinear physics perspective provides a framework to obtain insights into the nature of the COVID-19 dynamics during outbreak and subsiding stages and allows to discuss possible impacts of intervention measures. For example, the directions can be used to determine how different populations (e.g., exposed versus symptomatic individuals) vary in size relative to each other during the course of an epidemic. Moreover, the timeline of the computationally obtained stages can be compared with the history of the implementation of intervention measures to discuss the effectivity of such measures.

scholarly journals Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kaushik Dehingia ◽  
Hemanta Kumar Sarmah ◽  
Yamen Alharbi ◽  
Kamyar Hosseini
Keyword(s):  
Time Delay ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Cancer Model ◽  
Delay Effect ◽  
Discrete Time Delay ◽  
The Stability ◽  
Vital Parameters

AbstractIn this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system’s parameters. Some numerical simulations are presented to verify the obtained mathematical results.

scholarly journals Desain dan analisis pengaruh parameter PI dan variasi kecepatan pada respon sistem kontrol arah hadap prototype kendaraan listrik

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Afif Caesar Distara ◽  
Fatkhur Rohman
Keyword(s):  
Control System ◽  
Steady State ◽  
Electric Vehicles ◽  
Rise Time ◽  
Small Error ◽  
Settling Time ◽  
System Stability ◽  
Prototype System ◽  
Stability Parameters ◽  
The Stability

Electric vehicles are alternative vehicles that carry energy efficient. At this time the dominant vehicle uses ordinary wheels so that it will become an obstacle in the maneuver function that requires movement in various directions. With mechanum wheels the vehicle can move in various directions by adjusting the direction of rotation of each wheel. The problem is choosing the right control system for the control system needed by the vehicle. The purpose of this study is to determine and analyze the effect of variations in the value of PI (Proportional Integral) and speed of the vehicle to the stability response of the system to control the direction of prototype electric vehicles. This study method is an experiment that is by giving a treatment, then evaluating the effects caused by the research object. The results of this study can be concluded that the variation of PI constant values and speed variations have an effect on the stability parameters of the system, namely rise time, settling time, overshot, and steady state error. To get the best system stability response results can use the constant value PI Kp = 2; and Ki = 17; where the stability response of the system for direction control at each speed condition has a fairly good value with a fast rise time, fast settling time, small overshot and a small error steady state compared to other PI constant values in this study.Keywords: mechanum wheel, PI control, direction, prototype, system stability

Graphical Hopf Bifurcation of a Filippov HTLV-1 Model With Delay in Cytotoxic T Cells Response

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Elham Shamsara ◽  
Zahra Afsharnezhad ◽  
Elham Javidmanesh
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Bifurcation Theory ◽  
Cytotoxic T Cells ◽  
Dynamical Behavior ◽  
Bifurcation Theorem ◽  
Nyquist Criterion ◽  
The Stability ◽  
Frequency Domain Approach

In this paper, we present a discontinuous cytotoxic T cells (CTLs) response for HTLV-1. Moreover, a delay parameter for the activation of CTLs is considered. In fact, a system of differential equation with discontinuous right-hand side with delay is defined for HTLV-1. For analyzing the dynamical behavior of the system, graphical Hopf bifurcation is used. In general, Hopf bifurcation theory will help to obtain the periodic solutions of a system as parameter varies. Therefore, by applying the frequency domain approach and analyzing the associated characteristic equation, the existence of Hopf bifurcation by using delay immune response as a bifurcation parameter is determined. The stability of Hopf bifurcation periodic solutions is obtained by the Nyquist criterion and the graphical Hopf bifurcation theorem. At the end, numerical simulations demonstrated our results for the system of HTLV-1.

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