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Analysis of a type of nonsmooth dynamical systems
Chaos, Solitons & Fractals, 2006Abstract In this paper, a class of nonsmooth dynamical systems is analyzed. Extensive simulations reveal the chaotic behavior in these systems. By introducing a parameter, a chain of systems with one end being a linear stable system and the other being a chaotic system is constructed.
Yanping Lin +3 more
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Analysis of elastic systems with nonsmooth boundaries
2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA), 2017Often, for the construction of approximate analytical solutions for the components of the stress-strain state (SSS) of an elastic body, series on various systems of functions including trigonometric ones are used. They converge rapidly at the interior points of the elastic body while in the neighborhood of the boundary the rate of their convergence may
Dmitriy P. Goloskokov +1 more
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Nonsmooth Analysis in Control Theory: A Survey [PDF]
European Journal of Control, 2001 In the classical calculus of variations, the question of regularity (smoothness or otherwise of certain functions) plays a dominant role. This same issue, although it emerges in different guises, has turned out to be crucial in nonlinear control theory, in contexts as various as necessary conditions for optimal control, the existence of Lyapunov ...
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Nonsmooth analysis: Quasilinear approximations with orders
Nonlinear Analysis: Theory, Methods & Applications, 1996This paper proposes a new approach to nonsmooth analysis. The main idea is to generalize classical derivative through orders in the range. The setting of the approach is for a mapping \(f:X\to Y\), where \(X\) is a Banach space and \(Y\) is a complete Banach lattice.
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Nonsmooth analysis and parametric optimization
1990In an optimization problem that depends on parameters, an important issue is the effect that perturbations of the parameters can have on solutions to the problem and their associated multipliers. Under quite broad conditions the possibly multi-valued mapping that gives these elements in terms of the parameters turns out to enjoy a property of “proto ...
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1984
This survey of nonsmooth analysis sets out to prove an inverse function theorem for set-valued maps. The inverse function theorem for the more usual smooth maps plays a very important role in the solution of many problems in pure and applied analysis, and we can expect such an adaptation of this theorem also to be of great value. For example, it can be
Aubin, J.-P., Ekeland, I.
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This survey of nonsmooth analysis sets out to prove an inverse function theorem for set-valued maps. The inverse function theorem for the more usual smooth maps plays a very important role in the solution of many problems in pure and applied analysis, and we can expect such an adaptation of this theorem also to be of great value. For example, it can be
Aubin, J.-P., Ekeland, I.
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Miscellanies on Nonsmooth Analysis and Optimization
1985People who work in the area of research concerned with the analysis and optimization of novsmooth functions know they now have a panoply of “generalized subdifferentials” or “generalized gradients” at their disposal to treat optimization problems with nonsmooth data. In this short paper, which we wanted largely introductory, we develop some basic ideas
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Elements from Nonsmooth Analysis
2012The main subject of this book is the study of certain classes of nonsmooth equations. An unrenounceable device for the local analysis of smooth equations is the implicit function theorem. This theorem, however, exploits the approximation properties of the derivative of a smooth function and is thus not applicable in the nonsmooth case.
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