On the stability of equilibrium states of general fluids

1970 ◽  
Vol 36 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Bernard D. Coleman
Keyword(s):  
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

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.

scholarly journals Numerical Exploration of Kaldorian Interregional Macrodynamics: Enhanced Stability and Predominance of Period Doubling under Flexible Exchange Rates

2010 ◽  
Vol 2010 ◽  
pp. 1-29 ◽  
Author(s):  
Toichiro Asada ◽  
Christos Douskos ◽  
Vassilis Kalantonis ◽  
Panagiotis Markellos
Keyword(s):  
Exchange Rates ◽  
Government Expenditure ◽  
Period Doubling ◽  
Numerical Approach ◽  
Capital Movement ◽  
Dimensional Parameter ◽  
Stability Of Equilibrium ◽  
The Stability ◽  
Flexible Exchange Rates ◽  
Enhanced Stability

We present a discrete two-regional Kaldorian macrodynamic model with flexible exchange rates and explore numerically the stability of equilibrium and the possibility of generation of business cycles. We use a grid search method in two-dimensional parameter subspaces, and coefficient criteria for the flip and Hopf bifurcation curves, to determine the stability region and its boundary curves in several parameter ranges. The model is characterized by enhanced stability of equilibrium, while its predominant asymptotic behavior when equilibrium is unstable is period doubling. Cycles are scarce and short-lived in parameter space, occurring at large values of the degree of capital movementβ. By contrast to the corresponding fixed exchange rates system, for cycles to occur sufficient amount of trade is requiredtogetherwith high levels of capital movement. Rapid changes in exchange rate expectations and decreased government expenditure are factors contributing to the creation of interregional cycles. Examples of bifurcation and Lyapunov exponent diagrams illustrating period doubling or cycles, and their development into chaotic attractors, are given. The paper illustrates the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters.

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