Search results for "Mathematical analysis"

showing 10 items of 2409 documents

Singular hyperbolic systems

1999

We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsApplied MathematicsGeneral MathematicsMathematical analysisPhysics::Data Analysis; Statistics and ProbabilityHyperbolic systemsMathematicsProceedings of the American Mathematical Society
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Global attractors from the explosion of singular cycles

1997

Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsMathematical analysisAttractorApplied mathematicsGeneral MedicineDynamical systemMathematics::Geometric TopologyBifurcationHyperbolic systemsMathematicsComptes Rendus de l'Académie des Sciences - Series I - Mathematics
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Attracteurs de Lorenz de variété instable de dimension arbitraire

1997

Abstract We construct the first examples of flows with robust multidimensional Lorenz-like attractors: the singularity contained in the attractor may have any number of expanding eigenvalues, and the attractor remains transitive in a whole neighbourhood of the initial flow. These attractors support a Sinai-Ruelle-Bowen SRB-measure and, contrary to the usual (low-dimensional) Lorenz models, they have infinite modulus of structural stability.

Nonlinear Sciences::Chaotic DynamicsTransitive relationMathematics::Dynamical SystemsSingularityFlow (mathematics)Structural stabilityMathematical analysisAttractorNeighbourhood (graph theory)General MedicineLorenz systemEigenvalues and eigenvectorsMathematicsComptes Rendus de l'Académie des Sciences - Series I - Mathematics
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Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique

2003

This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T. The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newton’s method. For polynomial nonlinearities of cubic order, exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation o…

Nonlinear equationPolynomialMechanical EngineeringMathematical analysisSpectral densityCondensed Matter PhysicsPolynomialTrigonometric seriesNonlinear systemHarmonic balancesymbols.namesakeVibrations (mechanical)Mechanics of MaterialsJacobian matrix and determinantFourier transformNonlinear systemsymbolsVectorGalerkin methodFourier seriesNewton's methodMathematicsJournal of Applied Mechanics
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Quasi-sinusoidal oscillations in negative resistance devices with piece-wise analytical characteristics

1976

The second-order approximated solution of a negative resistance oscillator whose active device has a piece-wise analytical characteristic is presented. The frequency and the harmonic content of the oscillation waveform are obtained as functions of the circuit parameters and of the device bias.

Nonlinear oscillatorsControl theoryOscillationNegative resistanceMathematical analysisGeneral EngineeringHarmonicPiecewiseWaveformActive devicesMathematicsIEEE Transactions on Circuits and Systems
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Diffusion Equations with Finite Speed of Propagation

2007

In this paper we summarize some of our recent results on diffusion equations with finite speed of propagation. These equations have been introduced to correct the infinite speed of propagation predicted by the classical linear diffusion theory.

Nonlinear parabolic equationsLinear diffusionPhysicsMathematical analysisFinite volume method for one-dimensional steady state diffusionDiffusion (business)
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Optimal control for state constrained two-phase Stefan problems

1991

We give a new approach to state constrained control problems associated to non-degenerate nonlinear parabolic equations of Stefan type. We obtain uniform estimates for the violation of the constraints.

Nonlinear parabolic equationsMathematical analysisMathematics::Analysis of PDEsPhase (waves)State (functional analysis)Type (model theory)Optimal controlMathematics
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QUALITATIVE PROPERTIES OF THE SOLUTIONS OF A NONLINEAR FLUX-LIMITED EQUATION ARISING IN THE TRANSPORT OF MORPHOGENS

2011

In this paper we study some qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens in biological systems. Questions related to the existence of steady states, the finite speed of propagating fronts or the regularization in the interior of the support are studied from analytical and numerical points of view.

Nonlinear parabolic equationsNonlinear systemApplied MathematicsModeling and SimulationRegularization (physics)Mathematical analysisHeat equationMathematicsMathematical Models and Methods in Applied Sciences
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Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity

2011

In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.

Nonlinear systemAlgebra and Number TheoryApplied MathematicsMathematical analysisAttractorDissipative systemRandom compact setInitial value problemUniquenessRandom dynamical systemLipschitz continuityAnalysisMathematicsJournal of Difference Equations and Applications
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A parallel splitting up method and its application to Navier-Stokes equations

1991

A parallel splitting-up method (or the so called alternating-direction method) is proposed in this paper. The method not only reduces the original linear and nonlinear problems into a series of one dimensional linear problems, but also enables us to compute all these one dimensional linear problems by parallel processors. Applications of the method to linear parabolic problem, steady state and nonsteady state Navier-Stokes problems are given. peerReviewed

Nonlinear systemAlternating direction implicit methodSteady stateSeries (mathematics)business.industryApplied MathematicsMathematical analysisParabolic problemComputational fluid dynamicsNavier–Stokes equationsbusinessFinite element methodMathematicsApplied Mathematics Letters
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