Search results for "attractor"

showing 10 items of 162 documents

Counterexamples to the Kalman Conjectures

2018

In the paper counterexamples to the Kalman conjecture with smooth nonlinearity basing on the Fitts system, that are periodic solution or hidden chaotic attractor are presented. It is shown, that despite the fact that Kalman’s conjecture (as well as Aizerman’s) turned out to be incorrect in the case of n > 3, it had a huge impact on the theory of absolute stability, namely, the selection of the class of nonlinear systems whose stability can be studied with linear methods. peerReviewed

Barabanov systemsäätöteoriakaaosteoriamethodKalman conjectureFitts systempoint-mappinghidden attractor
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IWCFTA2012 Keynote Speech I - Hidden attractors in dynamical systems: From hidden oscillation in Hilbert-Kolmogorov, Aizerman and Kalman problems to …

2012

Summary form only given. In this survey an attempt is made to reflect the current trends in the synthesis of analytical and numerical methods to develop efficient analytical-numerical methods, based on harmonic linearization, applied bifurcation theory and numerical methods, for searching hidden oscillations.

Bifurcation theoryCurrent (mathematics)Dynamical systems theoryControl theoryNumerical analysisAttractorApplied mathematicsKalman filterHidden oscillationMathematicsElectronic circuit2012 Fifth International Workshop on Chaos-fractals Theories and Applications
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Attracteurs et bifurcations en dynamique holomorphe

2019

Bifurcations[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]BlendersAttractorsBifurcation[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]AttracteursMélangeur
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Buckling and nonlinear dynamics of elastically coupled double-beam systems

2016

Abstract This paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary s…

Buckling; Double-beam system; Global attractor; Nonlinear oscillations; Steady states; Mechanics of Materials; Mechanical Engineering; Applied MathematicsSteady statesBucklingApplied MathematicsMechanical Engineering010102 general mathematicsEigenfunctionDouble-beam system01 natural sciencesGlobal attractorNonlinear oscillations010101 applied mathematicsVibrationNonlinear systemClassical mechanicsBucklingMechanics of MaterialsAttractor0101 mathematicsNonlinear OscillationsFinite setBeam (structure)MathematicsInternational Journal of Non-Linear Mechanics
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Noise-induced behavioral change driven by transient chaos

2022

We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil…

CO-EXISTING ATTRACTORSVDP::Samfunnsvitenskap: 200::Økonomi: 210::Økonometri: 214General MathematicsApplied MathematicsGeneral Physics and AstronomyMULTISTABILITYBEHAVIORAL CHANGESNON-ATTRACTING CHAOTIC SETStatistical and Nonlinear PhysicsSTOCHASTIC DYNAMICSSTOCHASTIC SYSTEMSNON-ATTRACTING CHAOTIC SETSSTATISTICSVDP::Samfunnsvitenskap: 200::Økonomi: 210CHAOTIC SETSDYNAMICAL SYSTEMSNOISE-INDUCED TRANSITIONCRITICAL LINESCONSUMER BEHAVIORSTOCHASTIC MODELSCONFIDENCE REGIONFORECASTINGNOISE-INDUCED TRANSITIONSTRANSIENT CHAOS
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IFS attractors and Cantor sets

2006

Abstract We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R 3 such that every homeomorphism f of R 3 which preserves K coincides with the identity on K.

Cantor's theoremDiscrete mathematicsMathematics::Dynamical SystemsAntoine's necklaceCantor set[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]010102 general mathematicsMathematics::General TopologyCantor function01 natural sciences010101 applied mathematicsCombinatoricsNull setCantor setsymbols.namesakeMetric spaceAttractorsymbolsGeometry and Topology0101 mathematicsAntoine's necklaceCantor's diagonal argumentIterated function systemMathematicsTopology and its Applications
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Hidden and self-excited attractors in radiophysical and biophysical models

2017

One of the central tasks of investigation of dynamical systems is the problem of analysis of the steady (limiting) behavior of the system after the completion of transient processes, i.e., the problem of localization and analysis of attractors (bounded sets of states of the system to which the system tends after transient processes from close initial states). Transition of the system with initial conditions from the vicinity of stationary state to an attractor corresponds to the case of a self-excited attractor. However, there exist attractors of another type: hidden attractors are attractors with the basin of attraction which does not have intersection with a small neighborhoods of any equ…

Chua circuitskaaosteoriapancreatic beta-cellvirtapiiritattraktoritradiophysical generatoroskillaattoritbiofysiikkaNonlinear Sciences::Chaotic Dynamicshidden attractorsbifurkaatiosäteilyfysiikkamultistabilityself-excited attractorskatastrofiteoriamatemaattiset mallitdifferentiaaliyhtälöt
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A gallery of Chua's Attractors - Part VI

2007

Chua oscillator chaos n-scroll hyperchaotic and synchronized attractors computational approach
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Analytical-numerical methods for finding hidden oscillations in dynamical systems

2012

Chua's circuithidden attractorselektroniset piiritChuan piiriattraktoritdynaamiset systeemitlocalizationoskillaattoritlaskentamenetelmät
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Approximating hidden chaotic attractors via parameter switching.

2018

In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …

Class (set theory)Mathematics::Dynamical SystemsChaoticGeneral Physics and AstronomyFOS: Physical sciences01 natural sciences010305 fluids & plasmasSet (abstract data type)phase space methods0103 physical sciencesAttractorApplied mathematicsInitial value problemdifferentiaalilaskenta010301 acousticsMathematical PhysicsMathematicsApplied Mathematicsta111numerical approximationsStatistical and Nonlinear Physicschaotic systemsLorenz systemchaoticNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsNonlinear systemkaaosnumeerinen analyysinonlinear systemsChaotic Dynamics (nlin.CD)Chaos (Woodbury, N.Y.)
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