Graphical determination of the stability boundary in the real domain of an equilibrium point of a second-order nonlinear difference equation with a nonanalytic second member

1966 ◽  
Vol 2 (7) ◽  
pp. 239
Author(s):  
I. Gumowski ◽  
C. Mira
Keyword(s):  
Difference Equation ◽  
Equilibrium Point ◽  
Stability Boundary ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
The Real ◽  
Real Domain ◽  
The Stability

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

scholarly journals APLIKASI MODEL EPIDEMIK SEIAR-SEI PADA PENYEBARAN PENYAKIT MALARIA DENGAN INFEKSI ASIMTOMATIK DAN SUPER INFEKSI

2018 ◽  
Vol 15 (2) ◽  
pp. 67
Author(s):  
Stella Maryana Belwawin
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptomatic Infection ◽  
Endemic Equilibrium ◽  
Asymptomatic Infections ◽  
The Stability ◽  
Super Infection ◽  
The Basic Reproduction Number

AbstractThis aim of this study is to determine the point of equilibrium and analyze the stability of SEIAR-SEI model on malaria disease with asymptomatic infection, super infection and the effect of the mosquito's life cycle. This study also aim is to measure the sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes through the magnitude of . The method in this research is deductively, through several stage, such as  determination of disease-free equilibrium point and endemic equilibrium point, determination of basic reproduction number (), analyze of the basic reproduction number sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes. The endemic equilibrium point was obtained using rule of Descartes. The result show that the change in the value of parameter , , and  has effect on the basic reproduction number (). Treatment factors in the human population influence the elimination of malaria in a population. Whereas asymptomatic infection factors and the birth rate of adult mosquitoes influence the increase in malaria infection. Keywords:  Malaria, asymptomatic infection, super infection, basic reproduction number, rule of descrates. AbstrakPenelitian ini bertujuan menentukan titik keseimbangan dan menganalisis kestabilan dari model SEIAR_SEI pada penyakit malaria dengan pengaruh infeksi asimtomatik, super infeksi, dan siklus hidup nyamuk. Penelitian ini juga bertujuan mengukur tingkat sensitivitas penyebaran penyakit malaria terhadap parameter infeksi asimtomatik, laju pengobatan, serta laju kelahiran nyamuk.melalu besaran .  Metode yang digunakan dalam penelitian ini adalah metode deduktif dengan langkah-langkah : menentukan titik keseimbangan bebas penyakit dan endemik dan menentukan bilangan reproduksi dasar ). Analisis sensitivitas bilangan reproduksi dasar dilakukan terhadap parameter infeksi asimtomatik, pengobatan, dan laju kelahiran nyamuk. Tititk keseimbangan endemik diperoleh dengan aturan descrates. Hasil yang diperoleh menunjukkan parameter , , dan  berpengaruh terhadap bilangan reproduksi dasar (). Faktor pengobatan berpengaruh terhadap eliminasi penyakit malaria. Sedangkan faktor infeksi asimtomatik dan laju kelahiran nyamuk dewasa berpengaruh terhadap peningkatan infeksi penyakit malaria. Kata kunci: Malaria, Infeksi Asimtomatik, Super Infeksi, Bilangan Reproduksi Dasar, Aturan Descrates . 

scholarly journals Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Binbin Pei ◽  
Haojun Xu ◽  
Yuan Xue
Keyword(s):  
Equilibrium Point ◽  
External Disturbance ◽  
Stability Boundary ◽  
Wind Tunnel Test ◽  
Test Results ◽  
Theoretical Support ◽  
Effect Model ◽  
Short Period ◽  
The Stability ◽  
Period Model

Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA) around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.

scholarly journals Stability, Neimark–Sacker Bifurcation, and Approximation of the Invariant Curve of Certain Homogeneous Second-Order Fractional Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mirela Garić-Demirović ◽  
Samra Moranjkić ◽  
Mehmed Nurkanović ◽  
Zehra Nurkanović
Keyword(s):  
Difference Equation ◽  
Equilibrium Point ◽  
Asymptotic Approximation ◽  
Second Order ◽  
Invariant Curve ◽  
Unique Equilibrium ◽  
Fractional Difference ◽  
Global Character ◽  
Fractional Difference Equation

We investigate the local and global character of the unique equilibrium point and boundedness of the solutions of certain homogeneous fractional difference equation with quadratic terms. Also, we consider Neimark–Sacker bifurcations and give the asymptotic approximation of the invariant curve.

STABILITY BOUNDARY CHARACTERIZATION OF NONLINEAR AUTONOMOUS DYNAMICAL SYSTEMS IN THE PRESENCE OF A SUPERCRITICAL HOPF EQUILIBRIUM POINT

2013 ◽  
Vol 23 (12) ◽  
pp. 1350196 ◽  
Author(s):  
JOSAPHAT R. R. GOUVEIA ◽  
FABÍOLO MORAES AMARAL ◽  
LUÍS F. C. ALBERTO
Keyword(s):  
Dynamical Systems ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Boundary ◽  
Complete Characterization ◽  
Center Manifolds ◽  
The Stability ◽  
Hyperbolic Equilibrium ◽  
Autonomous Dynamical Systems

A complete characterization of the boundary of the stability region (or area of attraction) of nonlinear autonomous dynamical systems is developed admitting the existence of a particular type of nonhyperbolic equilibrium point on the stability boundary, the supercritical Hopf equilibrium point. Under a condition of transversality, it is shown that the stability boundary is comprised of all stable manifolds of the hyperbolic equilibrium points lying on the stability boundary union with the center-stable and\or center manifolds of the type-k, k ≥ 1, supercritical Hopf equilibrium points on the stability boundary.

On the spin-up and spin-down of a rotating fluid. Part 2. Measurements and stability

1976 ◽  
Vol 77 (4) ◽  
pp. 709-735 ◽  
Author(s):  
Patrick D. Weidman
Keyword(s):  
Stability Boundary ◽  
Fluid Motion ◽  
Azimuthal Velocity ◽  
Laser Doppler Velocimeter ◽  
Rotating Fluid ◽  
Constant Acceleration ◽  
Centrifugal Instability ◽  
The Stability ◽  
Theoretical Results

Measurements of the azimuthal velocity inside a cylinder which spins up or spins down at constant acceleration were obtained with a laser-Doppler velocimeter and compared with the theoretical results presented in part 1. Velocity profiles near the wave front in spin-up indicate that the velocity discontinuity given by the inviscid Wedemeyer model is smoothed out in a shear layer whose thickness varies with radius and time but scales with hE1/4Ω. The spin-down profiles are always in excellent agreement with theory when the flow is stable. Visualization studies with aluminium tracers have made possible the determination of the stability boundary for Ekman spiral waves (principally type II waves) observed on the cylinder end walls during spin-up. For spin-down to rest the flow always experienced a centrifugal instability which ultimately disrupted the interior fluid motion.

Effiziente Ermittlung von Stabilitätsgrenzen*/Detection of stability boundaries during milling

2017 ◽  
Vol 107 (05) ◽  
pp. 313-317
Author(s):  
C. Prof. Brecher ◽  
P. Chavan ◽  
A. Epple
Keyword(s):  
Stability Boundary ◽  
Spindle Speed ◽  
Wird Eine ◽  
Chatter Detection ◽  
Speed Variation ◽  
Spindle Speed Variation ◽  
Detection Software ◽  
The Stability ◽  
Stability Limits

Um Stabilitätskarten für Fräsprozesse effizient zu erstellen, bietet sich eine kontinuierliche Variation der Drehzahl an. Jedoch kann die permanente Änderung der Drehzahl zu einer Verfälschung der tatsächlichen Stabilitätsgrenzen führen. Dieser Fachbeitrag analysiert den Einfluss der Spindeldrehzahlvariation auf die Stabilitätsgrenzen bei Fräsversuchen mit verschiedenen Drehzahlbeschleunigungen. Für das Erkennen der Stabilitätsübergänge wird eine Rattererkennungssoftware eingesetzt.   Milling with varying spindle speed allows an efficient determination of instabilities. However, spindle speed variation may also influence the actual stability boundary with constant spindle speed. This paper analyzes the influence of spindle speed variation on the stability limits by evaluating milling trials at different spindle accelerations. For the detection of instability and stability during cutting trials, a time-domain chatter detection software was enhanced, validated and implemented.

scholarly journals Monotonicity of Eventually Positive Solutions for a Second Order Nonlinear Difference Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huiqin Chen ◽  
Zhen Jin ◽  
Shugui Kang
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Difference Equation ◽  
Monotone Solutions

We derive several sufficient conditions for monotonicity of eventually positive solutions on a class of second order perturbed nonlinear difference equation. Furthermore, we obtain a few nonexistence criteria for eventually positive monotone solutions of this equation. Examples are provided to illustrate our main results.

The Stability of the Second-Order Model of the Damping Single Maching Infinite Bus Bar System

2013 ◽  
Vol 457-458 ◽  
pp. 1004-1007
Author(s):  
Hong Ying Luo ◽  
Jun Liu ◽  
Long Xing Li
Keyword(s):  
Lyapunov Function ◽  
Equilibrium Point ◽  
Single Machine ◽  
Function Method ◽  
Second Order ◽  
Order Model ◽  
Lyapunov Function Method ◽  
Single Machine Infinite Bus ◽  
The Stability ◽  
Second Order Model

This paper studies the stability of the second-order model of the damping single machine infinite bus bar system,by constructing a suitable Lyapunov function method,and discuss the stability of the equilibrium point,then obtains the attractive area.

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