Search results for "Random dynamical system"

showing 8 items of 8 documents

On a Planar Dynamical System Arising in the Network Control Theory

2016

We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

0301 basic medicineDynamical systems theoryPhase portraitattractor selection020206 networking & telecommunicationsphase portraits02 engineering and technologyDynamical systemnetworks controldynamical systemLinear dynamical system03 medical and health sciences030104 developmental biologyProjected dynamical systemControl theoryModeling and SimulationAttractor0202 electrical engineering electronic engineering information engineeringQA1-939Statistical physicsLimit setRandom dynamical systemAnalysisMathematicsMathematicsMathematical Modelling and Analysis
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ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS

2010

In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.

Dynamical systems theoryApplied MathematicsModeling and SimulationLattice (order)AttractorMathematical analysisLimit setRandom dynamical systemEngineering (miscellaneous)Backward Euler methodNon-Newtonian fluidMathematicsLinear dynamical systemInternational Journal of Bifurcation and Chaos
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Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities

2012

AbstractIn this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a multiplicative 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.

Dynamical systems theoryApplied MathematicsRandom attractorsMathematical analysisMultiplicative noisePullback attractorLipschitz continuityMultiplicative noiseSet-valued dynamical systemLinear dynamical systemProjected dynamical systemStochastic lattice differential equationsAttractorRandom dynamical systemAnalysisMathematicsJournal of Differential Equations
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Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents

2021

Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global at…

Lyapunov functionGeneral MathematicsChaoticFOS: Physical sciencesGeneral Physics and AstronomyattraktoritAbsorbing set (random dynamical systems)Lyapunov exponentInstabilitysymbols.namesakeDimension (vector space)AttractorApplied mathematicsEntropy (information theory)taloudelliset mallitdynaamiset systeemitMathematicskaaosteoriaApplied MathematicsLyapunov exponentstaloudelliset ennusteetkausivaihtelutStatistical and Nonlinear PhysicsAbsorbing setNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsMid-size firm modelLyapunov dimensionsymbolsUnstable periodic orbitChaotic Dynamics (nlin.CD)Chaos, Solitons & Fractals
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Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

2008

In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …

Mathematical optimizationDynamical systems theoryCharacteristic function (probability theory)Stochastic processMechanical EngineeringFokker-Planck equationProbability density functionLévy white noiseBuilding and ConstructionWhite noiseStable processstochastic differential calculusymbols.namesakeAdditive white Gaussian noiseMechanics of MaterialssymbolsStatistical physicssub-Gaussian white noise.Settore ICAR/08 - Scienza Delle CostruzioniRandom dynamical systemCivil and Structural EngineeringMathematicsStructural Engineering and Mechanics
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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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Attractors for non-autonomous retarded lattice dynamical systems

2015

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Statistics and ProbabilityDifferential equations with delayDynamical systems theoryNon-autonomous systemslattice dynamical systemsPullback attractorHamiltonian systemLinear dynamical systemProjected dynamical systemAttractorQA1-939pullback attractorMathematicsNumerical AnalysisApplied MathematicsMathematical analysisdifferential equations with delaynon-autonomous systemsClassical mechanicsLattice dynamical systemsPullback attractorset-valued dynamical systemsSet-valued dynamical systemsLimit setRandom dynamical systemMathematicsAnalysis
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On a rough perturbation of the Navier-Stokes system and its vorticity formulation

2019

We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We present a framework for a well-posedness analysis of the system. In particular, we define an intrinsic notion of solution based on ideas from the rough path theory and study the system in an equivalent vorticity formulation. In two space dimensions, we prove that well-posedness and enstrophy balance holds. Moreover, we derive rough path continuity of the equation, which yields a Wong-Zakai result for Brownian driving paths, and show that for a large class of driving signals, the system generates a continuous rando…

Statistics and ProbabilityRough pathMathematical analysisProbability (math.PR)VorticityEnstrophyMomentumPhysics::Fluid DynamicsMathematics - Analysis of PDEsInviscid flowFOS: MathematicsLimit (mathematics)Statistics Probability and UncertaintyRandom dynamical systemBrownian motionMathematics - ProbabilityMathematicsAnalysis of PDEs (math.AP)
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