Results 11 to 20 of about 2,287 (271)
DIFFERENTIABLE DYNAMICAL SYSTEMS [PDF]
Bulletin of the American Mathematical Society, 1967 This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a homomorphism G→Diff(M) such that the induced map G×M→M is differentiable.
Steve Smale
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Differentiable dynamical systems and the problem of turbulence [PDF]
Bulletin of the American Mathematical Society, 1981 Summary: The paper is a review presented at the Symposium on the Mathematical Heritage of Henry Poincaré in 1980. The author discusses different theories of turbulence. He explains the way dynamical systems appear in the study of Navier-Stokes equation and describes the connection between the turbulence and the ``strange'' attractors theory. The author
David Ruelle
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Commentary on “Differentiable dynamical systems” by Stephen Smale [PDF]
Bulletin of the American Mathematical Society, 2018 Immediately following the commentary below, this previously published article is reprinted in its entirety: Stephen Smale, “Differentiable dynamical systems”, Bull. Amer. Math. Soc. 73 (1967), no. 6, 747–817.
Maciej Zworski
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Extended Differential Balancing for Nonlinear Dynamical Systems
IEEE Control Systems Letters, 2022 In this paper, we construct extended balancing theory for nonlinear systems in the contraction framework. At first, we introduce the concept of the extended differential observability Gramian and inverse of the extended differential controllability Gramian for nonlinear dynamical systems and show their correspondence with generalized differential ...
Arijit Sarkar, Jacquelien M. A. Scherpen
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Dynamics of the polynomial differential systems
Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2023 In general, there are several free parameters. By using a method introduced in a previous paper, we obtain a sequence of algebraic a proximations to the bifurcationsets,in the parameter ...
Feneniche Fatima, Rezaoui Med Salem
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PRX Quantum, 2021 Quantum control, which refers to the active manipulation of physical systems described by the laws of quantum mechanics, constitutes an essential ingredient for the development of quantum technology.
Luuk Coopmans +4 more
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Entropy, 2012 In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-
Wassim M. Haddad
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Bayesian Differential Privacy for Linear Dynamical Systems [PDF]
IEEE Control Systems Letters, 2022 Differential privacy is a privacy measure based on the difficulty of discriminating between similar input data. In differential privacy analysis, similar data usually implies that their distance does not exceed a predetermined threshold. It, consequently, does not take into account the difficulty of distinguishing data sets that are far apart, which ...
Genki Sugiura, Kaito Ito, Kenji Kashima
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Entropy, 2014 Advances in neuroscience have been closely linked to mathematical modeling beginning with the integrate-and-fire model of Lapicque and proceeding through the modeling of the action potential by Hodgkin and Huxley to the current era.
Wassim M. Haddad +2 more
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Robust Stability of a Class of Uncertain Lur'e Systems of Neutral Type
Abstract and Applied Analysis, 2012 This paper deals with the problem of stability for a class of Lur’e systems with interval time-varying delay and sector-bounded nonlinearity. The interval time-varying delay function is not assumed to be differentiable.
W. Weera, P. Niamsup
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