On the stability of equilibrium states of the dynamical systems in critical cases

2021 ◽  
Vol 569 ◽  
pp. 125787
Author(s):  
Alexandr A. Barsuk ◽  
Florentin Paladi
Keyword(s):  
Dynamical Systems ◽  
Equilibrium States ◽  
Stability Of Equilibrium ◽  
The Stability

On the stability of equilibrium states of finite classical systems

1975 ◽  
Vol 16 (6) ◽  
pp. 1284-1287 ◽  
Author(s):  
Joel L. Lebowitz ◽  
Michael Aizemann ◽  
Sheldon Goldstein
Keyword(s):  
Equilibrium States ◽  
Classical Systems ◽  
Stability Of Equilibrium ◽  
The Stability

On Stability of N-Dimensional Dynamical Systems

2009 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Distance Function ◽  
Relative Distance ◽  
Stability Of Equilibrium ◽  
The Stability

This paper presents a theory of the stability of equilibrium in dynamical systems. The measuring function is introduced through a relative distance function. The kth -order, G – functions at the equi-measuring function surface and the increment of the equi-measuring function are introduced. Based on the kth -order, G – functions, a theory for the stability of dynamical system is presented, including the definitions and theorems.

ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR AMBIPOLAR PLASMAS

2004 ◽  
Vol 14 (09) ◽  
pp. 1361-1399 ◽  
Author(s):  
V. GIOVANGIGLI ◽  
B. GRAILLE
Keyword(s):  
Partial Differential Equations ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Null Space ◽  
Current Model ◽  
Debye Length ◽  
Equilibrium States ◽  
Electron Mass ◽  
Partial Differential ◽  
Stability Of Equilibrium

We investigate a system of partial differential equations modeling ambipolar plasmas. The ambipolar — or zero current — model is obtained from general plasmas equations in the limit of vanishing Debye length. In this model, the electric field is expressed as a linear combination of macroscopic variable gradients. We establish that the governing equations can be written as a symmetric form by using entropic variables. The corresponding dissipation matrices satisfy the null space invariant property and the system of partial differential equations can be written as a normal form, i.e. in the form of a symmetric hyperbolic–parabolic composite system. By properly modifying the chemistry source terms and/or the diffusion matrices, asymptotic stability of equilibrium states is established and decay estimates are obtained. We also establish the continuous dependence of global solutions with respect to vanishing electron mass.

Sign in / Sign up

Export Citation Format

Share Document