A stability theorem for dissipative magnetohydrodynamic equilibria

1982 ◽  
Vol 60 (5) ◽  
pp. 640-643 ◽  
Author(s):  
J. Teichmann
Keyword(s):  
Global Stability ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Lagrangian System ◽  
Dissipative Operators ◽  
Isentropic Flow ◽  
Liapunov Method ◽  
First Time ◽  
Two Fluid

The global stability of stationary equilibria of dissipative magnetohydrodynamics is studied using the direct Liapunov method. Sufficient conditions for stability of the linearized Euler–Lagrangian system with the full dissipative operators are given for the first time. The case of the two-fluid isentropic flow is discussed.

scholarly journals Persistence in expansive systems

1983 ◽  
Vol 3 (4) ◽  
pp. 567-578 ◽  
Author(s):  
Jorge Lewowicz
Keyword(s):  
Structural Stability ◽  
Compact Manifold ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Dynamical Features

AbstractWe give some sufficient conditions for an expansive diffeomorphism ƒ of a compact manifold to be such that every neighbouring diffeomorphism shows, roughly, all the dynamical features of ƒ. These results are then applied to prove a structural stability theorem for pseudo-Anosov maps.

scholarly journals Existence and global stability of periodic solution for delayed discrete high-order Hopfield-type neural networks

2005 ◽  
Vol 2005 (3) ◽  
pp. 281-297 ◽  
Author(s):  
Hong Xiang ◽  
Ke-Ming Yan ◽  
Bai-Yan Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Global Stability ◽  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
High Order ◽  
Priori Estimates

By using coincidence degree theory as well as a priori estimates and Lyapunov functional, we study the existence and global stability of periodic solution for discrete delayed high-order Hopfield-type neural networks. We obtain some easily verifiable sufficient conditions to ensure that there exists a unique periodic solution, and all theirs solutions converge to such a periodic solution.

scholarly journals Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Yuanke Li
Keyword(s):  
Global Stability ◽  
Toxic Effect ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Competitive System ◽  
Comparison Arguments ◽  
Double Time

We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

Counter differential rigid-rotation equilibrium of electrically non-neutral two-fluid plasma with finite pressure

2021 ◽  
Vol 87 (4) ◽  
Author(s):  
Y. Nakajima ◽  
H. Himura ◽  
A. Sanpei
Keyword(s):  
Ion Plasma ◽  
Counter Rotation ◽  
Fluid Velocities ◽  
Two Component ◽  
Component Plasma ◽  
Ion Cloud ◽  
Diamagnetic Drift ◽  
First Time ◽  
Two Fluid ◽  
Two Fluid Plasma

We derive the two-dimensional counter-differential rotation equilibria of two-component plasmas, composed of both ion and electron ( $e^-$ ) clouds with finite temperatures, for the first time. In the equilibrium found in this study, as the density of the $e^{-}$ cloud is always larger than that of the ion cloud, the entire system is a type of non-neutral plasma. Consequently, a bell-shaped negative potential well is formed in the two-component plasma. The self-electric field is also non-uniform along the $r$ -axis. Moreover, the radii of the ion and $e^{-}$ plasmas are different. Nonetheless, the pure ion as well as $e^{-}$ plasmas exhibit corresponding rigid rotations around the plasma axis with different fluid velocities, as in a two-fluid plasma. Furthermore, the $e^{-}$ plasma rotates in the same direction as that of $\boldsymbol {E \times B}$ , whereas the ion plasma counter-rotates overall. This counter-rotation is attributed to the contribution of the diamagnetic drift of the ion plasma because of its finite pressure.

Reconstruction of a convolution operator from the right-hand side on the semiaxis

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Anatoly F. Voronin
Keyword(s):  
Inverse Problem ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Explicit Formulas ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient ◽  
Operator Kernel ◽  
Problem Solvability

AbstractIn this paper, a Volterra integral equation of the first kind in convolutions on the semiaxis when the integral operator kernel and the right-hand side of the equation have a bounded support is considered. An inverse problem of reconstructing the solution to the equation and the integral operator kernel from values of the right-hand side is formulated. Necessary and sufficient conditions for the inverse problem solvability are obtained. A uniqueness and stability theorem is proved. Explicit formulas for reconstruction of the solution and kernel are obtained.

Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Najah F. Jasim
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
External Disturbances ◽  
Fast Switching ◽  
Nonlinear Switched Systems ◽  
Arbitrary Switching

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

scholarly journals Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model

2005 ◽  
Vol 2005 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

We first give sufficient conditions for the permanence of nonautonomous discrete ratio-dependent predator-prey model. By linearization of the model at positive solutions and construction of Lyapunov function, we also obtain some conditions which ensure that a positive solution of the model is stable and attracts all positive solutions.

scholarly journals Global Stability of Almost Periodic Solution of a Class of Neutral-Type BAM Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Tetie Pan ◽  
Bao Shi ◽  
Jian Yuan
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Almost Periodic Solution ◽  
Bam Neural Networks ◽  
Almost Periodic ◽  
Globally Exponential Stability ◽  
First Time

A class of BAM neural networks with variable coefficients and neutral delays are investigated. By employing fixed-point theorem, the exponential dichotomy, and differential inequality techniques, we obtain some sufficient conditions to insure the existence and globally exponential stability of almost periodic solution. This is the first time to investigate the almost periodic solution of the BAM neutral neural network and the results of this paper are new, and they extend previously known results.

scholarly journals Global Stability of Humoral Immunity HIV Infection Models with Chronically Infected Cells and Discrete Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-25
Author(s):  
A. M. Elaiw ◽  
N. A. Alghamdi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Humoral Immune ◽  
Infection Models ◽  
Existence And Stability ◽  
Discrete Delays ◽  
Infected Cells ◽  
Theoretical Results

We study the global stability of three HIV infection models with humoral immune response. We consider two types of infected cells: the first type is the short-lived infected cells and the second one is the long-lived chronically infected cells. In the three HIV infection models, we modeled the incidence rate by bilinear, saturation, and general forms. The models take into account two types of discrete-time delays to describe the time between the virus entering into an uninfected CD4+T cell and the emission of new active viruses. The existence and stability of all equilibria are completely established by two bifurcation parameters,R0andR1. The global asymptotic stability of the steady states has been proven using Lyapunov method. In case of the general incidence rate, we have presented a set of sufficient conditions which guarantee the global stability of model. We have presented an example and performed numerical simulations to confirm our theoretical results.

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