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Differential Stability in Nonlinear Programming
SIAM Journal on Control and Optimization, 1977This paper consists of a study of stability and differential stability in nonconvex programming. For a program with equality and inequality constraints, upper and lower bounds are estimated for the potential directional derivatives of the perturbation function (or the extremal-value function).
Gauvin, Jacques, Tolle, Jon W.
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Stochastic Stability of Nonlinear Oscillators
SIAM Journal on Applied Mathematics, 1988The authors study the stability behavior of a non-linear oscillator parametrically excited by a stationary Markov process. They modify the notion of stability by considering \(H(E_ 0)=\sup_{t>0}E(t,E_ 0)\), where \(E(t)=U(x(t))+\dot x(t)^ 2\) is the sum of potential and kinetic energy, rather than the usual \(\sup_{t>0}| \vec x(t,\vec x_ 0)|\), where \(
Kłosek-Dygas, M. M. +2 more
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Nonlinear stability for Eady’s model
Applied Mathematics and Mechanics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Yong-Ming, Qiu, Ling-Cun
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The Physics of Fluids, 1976
The nonlinear energy theorem of Rosenbluth for helically symmetric tokamak magnetohydrodynamic motions is used to find nonlinear corrections to the linear stability of kink modes. Near marginal stability these corrections are important and give a finite amplitude threshold for instability. Cases are also found in which a mode saturates at low amplitude,
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The nonlinear energy theorem of Rosenbluth for helically symmetric tokamak magnetohydrodynamic motions is used to find nonlinear corrections to the linear stability of kink modes. Near marginal stability these corrections are important and give a finite amplitude threshold for instability. Cases are also found in which a mode saturates at low amplitude,
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Bifurcation in Nonlinear Hydrodynamic Stability
SIAM Review, 1975The appearance of secondary motions in a viscous fluid field can be understood to some extent as a bifurcation phenomenon with exchange of stability between the basic and the secondary flow. This article summarizes the main mathematical results of bifurcation and stability in hydrodynamic stability theory so far obtained.
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EXTERNAL STABILITY OF NONLINEAR SYSTEMS
IFAC Proceedings Volumes, 1995Abstract The aim of this note is to present and characterize a notion of external stability for nonlinear systems. Moreover, relationship with appropriate internal stability properties are discussed. Finally, we give a partial answer to the problem of external stabilizability by means of feedback.
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Selectivity and Stability via Dendritic Nonlinearity
Neural Computation, 2007Inspired by recent studies regarding dendritic computation, we constructed a recurrent neural network model incorporating dendritic lateral inhibition. Our model consists of an input layer and a neuron layer that includes excitatory cells and an inhibitory cell; this inhibitory cell is activated by the pooled activities of all the excitatory cells ...
Morita, Kenji +2 more
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STABILIZATION OF NONLINEAR PARABOLIC EQUATIONS
IFAC Proceedings Volumes, 1983Abstract We are concerned with the possibility of constructing implementable feedback control laws to stabilize ů + Au = f(u), primarily through the boundary conditions. Semigroup methods are employed to reduce the semi- linear problem to a linear one, to show stabilizability of certain parabolic problems by feedback and, finally, to show for the one-
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Stability of Nonlinear Computing Schemes
SIAM Journal on Numerical Analysis, 1969by deriving necessary and sufficient conditions for the stability of nonlinear computing schemes. In ? 1, we motivate the concept of stability to be used here and provide the basic definitions. In ? 2, we prove the main theorem on stability which relates stability to conditions on the Frechet derivatives of the operators. As corollaries of this theorem
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Nonlinear Systems: Stability Analysis
IEEE Transactions on Systems, Man, and Cybernetics, 1982This work, which is part of the benchmark series in electrical engineering and computer science, is a compilation of the research papers representing the major advances in the area of nonlinear systems stability. It contains a total of 28 papers that pertain to both Lyapunov-like approach applied to ordinary differential equations and functional ...
J. K. Aggarwal +2 more
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