A Saddle Value Characterization of Fan's Equilibrium Points

1982 ◽  
Author(s):  
A. Charnes ◽  
K. O. Kortanek ◽  
V. Lovegren
Keyword(s):  
Equilibrium Points ◽  
Saddle Value

Bifurcations and Chaos in a PD-Controlled Pendulum

1998 ◽  
Vol 120 (1) ◽  
pp. 146-149 ◽  
Author(s):  
Joaqui´n Alvarez ◽  
Fernando Verduzco
Keyword(s):  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Equilibrium Points

The complex dynamics of a pendulum controlled by a Proportional-Derivative (PD) compensator are analyzed. A classification of equilibrium points and the characterization of their bifurcations is also presented. It is shown that the controlled pendulum may exhibit a chaotic behavior when the desired position is periodic and the proportional gain and total dissipation are small enough.

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.

scholarly journals On Characterization of Optimal Control Model of Whooping Cough

2021 ◽  
pp. 175-188
Author(s):  
A. S. Ismail ◽  
Y. O. Aderinto
Keyword(s):  
Optimal Control ◽  
Whooping Cough ◽  
Equilibrium Points ◽  
Public Health Problem ◽  
Sweep Method ◽  
Optimal Control Strategy ◽  
Runge Kutta Method ◽  
Disease Free ◽  
Forward Backward Sweep Method

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

scholarly journals Stability of Fuzzy Dynamical Systems via Lyapunov Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Abdelati El Allaoui ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Dynamical Systems ◽  
Initial Value Problems ◽  
Lyapunov Functions ◽  
Equilibrium Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial Value ◽  
Necessary And Sufficient ◽  
Fuzzy Dynamical Systems

The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.

scholarly journals Stability analysis and prevention strategies of tobacco smoking model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ebraheem Alzahrani ◽  
Anwar Zeb
Keyword(s):  
Tobacco Smoking ◽  
Equilibrium Points ◽  
Research Work ◽  
Optimal Level ◽  
Proposed Model ◽  
Fourth Order Method ◽  
Nsfd Scheme ◽  
The Pontryagin Maximum Principle ◽  
Hurwitz Theorem

AbstractThis research work is related to a tobacco smoking model having a significance class of users of tobacco in the form of snuffing. For this purpose, the formulation of the model containing snuffing class is presented; then the equilibrium points as regards being smoking free and smoking positive are discussed. The Hurwitz theorem is used for finding the local stability of the model and Lyaponov function theory is used for the search of global stability. We use different controls for control of smoking and the Pontryagin maximum principle for characterization of the optimal level. For the solution of the proposed model, a nonstandard finite difference (NSFD) scheme and the Runge–Kutta fourth order method are used. Finally, some numerical results are presented for control and without control systems with the help of MATLAB.

scholarly journals Subcritical Hopf Equilibrium Points in Boundary of the Stability Region

2016 ◽  
Vol 17 (2) ◽  
pp. 211 ◽  
Author(s):  
Josaphat Ricardo Ribeiro Gouveia Jr ◽  
Fabíolo Moraes Amaral ◽  
Luís Fernando Costa Alberto
Keyword(s):  
Stability Region ◽  
Equilibrium Points ◽  
Transversality Condition ◽  
Complete Characterization ◽  
Stable Manifolds ◽  
The Stability ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point ◽  
Autonomous Dynamical Systems

A complete characterization of the boundary of the stability region of a class of nonlinear autonomous dynamical systems is developed admitting the existence of Subcritical Hopf nonhyperbolic equilibrium points on the boundary of the stability region. The characterization of the stability region developed in this paper is an extension of the characterization already developed in the literature, which considers only hyperbolic equilibrium point. Under the transversality condition, it is shown the boundary of the stability region is comprised of the stable manifolds of all equilibrium points on the boundary of the stability region, including the stable manifolds of the subcritical Hopf equilibrium points of type k, with 0<=k<=(n-2), which belong to the boundary of the stability region.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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