Stability of parallel flow of a multi-component cylindrical plasma to electrostatic perturbations

1981 ◽  
Vol 26 (2) ◽  
pp. 369-383
Author(s):  
R. Lucas
Keyword(s):  
Normal Mode ◽  
Axial Velocity ◽  
Sufficient Conditions ◽  
Parallel Flow ◽  
Zeroth Order ◽  
Unperturbed State ◽  
Plasma Component ◽  
Cylindrical Plasma ◽  
The Stability ◽  
System Variables

Sufficient conditions for the stability of parallel flow of a warm N-component cylindrical plasma to electrostatic perturbations are obtained. In the unperturbed state the jth plasma component is assumed to have axial velocity Vj0(r), r being the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the zeroth-order equations. The L2-norms of certain system variables are shown to be bounded uniformly in time. Circle theorems are obtained for the complex eigenfrequencies of any normal mode.

The stability of parallel flow of a multi-component plasma

1980 ◽  
Vol 24 (2) ◽  
pp. 251-264 ◽  
Author(s):  
R. J. Lucas
Keyword(s):  
Gravitational Field ◽  
Sufficient Conditions ◽  
Parallel Flow ◽  
Liapunov Functional ◽  
Multicomponent Plasma ◽  
Plane Parallel ◽  
External Gravitational Field ◽  
Component Plasma ◽  
The Stability ◽  
System Variables

A Liapunov functional is constructed for the plane parallel flow of a multicomponent plasma in an external gravitational field. Sufficient conditions for stability to electrostatic perturbations are obtained. The L2-norms of certain system variables are shown to be bounded uniformly in time.

The stability of a rotating flow in the presence of an axial and a toroidal magnetic field

1977 ◽  
Vol 79 (3) ◽  
pp. 417-434 ◽  
Author(s):  
Chao-Ho Sung
Keyword(s):  
Magnetic Field ◽  
Normal Mode ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Toroidal Magnetic Field ◽  
Initial Value ◽  
Coaxial Cylinders ◽  
The Stability ◽  
Westward Drift ◽  
Axisymmetric Perturbations

Making a normal-mode assumption, we shall investigate stability with respect to non-axisymmetric perturbations of an inhomogeneous incompressible fluid rotating between two perfectly conducting, infinite, coaxial cylinders in the presence of an axial and a toroidal magnetic field. We shall establish sufficient conditions for stability, discuss the westward-drift nature of unstable modes and estimate upper bounds on the azimuthal phase speeds and growth rates. There will also be a discussion of the validity of the sufficient conditions for stability when the normal-mode assumption is not made, so that the stability is based on an initial-value problem.

Coexistence Phenomenon in Autoparametric Excitation of Two Degree of Freedom Systems

2005 ◽  
Author(s):  
Geoffrey Recktenwald ◽  
Richard Rand
Keyword(s):  
Normal Mode ◽  
Sufficient Conditions ◽  
Degree Of Freedom ◽  
Stability Of Motion ◽  
Nonlinear Normal Mode ◽  
Parametrically Excited ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

Coexistence phenomenon refers to the absence of expected tongues of instability in parametrically excited systems. In this paper we obtain sufficient conditions for coexistence to occur in the generalized Ince equation: (1+a1cost+a2cos2t)v¨+(b1sint+b2sin2t)v˙+(δ+c1cost+c2cos2t)v=0 The results are applied to the stability of motion of a nonlinear normal mode, the x-mode, in a class of conservative two degree of freedom systems.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

scholarly journals Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Computer Network ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Form Theory ◽  
Worm Model ◽  
The Stability

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

Sign in / Sign up

Export Citation Format

Share Document