Search results for "Lorenz-like system"

showing 6 items of 6 documents

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

2015

Currently it is being actively discussed the question of the equivalence of various Lorenzlike systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed. peerReviewed

Chen systemLorenz systemLorenz-like systemsLu systemLyapunov exponentChaotic analog of 16th Hilbert problem
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Hidden attractors on one path : Glukhovsky-Dolzhansky, Lorenz, and Rabinovich systems

2017

In this report, by the numerical continuation method we visualize and connect hidden chaotic sets in the Glukhovsky-Dolzhansky, Lorenz and Rabinovich systems using a certain path in the parameter space of a Lorenz-like system.

Computer sciencechaosChaoticFOS: Physical sciencesPhysics::Data Analysis; Statistics and ProbabilityParameter space01 natural sciences010305 fluids & plasmasRabinovich systemLorenz system0103 physical sciencesAttractorGlukhovsky–Dolzhansky systemApplied mathematics010301 acousticsEngineering (miscellaneous)kaaosteoriaApplied Mathematicsta111Lorenz-like systemNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsNumerical continuationModeling and SimulationPath (graph theory)numeerinen analyysiChaotic Dynamics (nlin.CD)hidden attractorInternational Journal of Bifurcation and Chaos
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On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

2015

Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a,b, 2014b,c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.

FOS: Physical sciencesLyapunov exponentLorenz-like systemsLu systemChaotic analog of 16th Hilbert problemReduction (complexity)symbols.namesakeChenDevelopment (topology)Lorenz systemChaotic systemsCalculusApplied mathematicsEquivalence (measure theory)MathematicsbiologyApplied Mathematicsta111Lorenz systembiology.organism_classificationNonlinear Sciences - Chaotic DynamicsComputational MathematicsChen systemsymbolsChaotic Dynamics (nlin.CD)Lyapunov exponentApplied Mathematics and Computation
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Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity

2015

Abstract In this paper a Lorenz-like system, describing convective fluid motion in rotating cavity, is considered. It is shown numerically that this system, like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for the considered system, unlike the classical Lorenz system, along with self-excited attractor a hidden attractor can be localized. Analytical-numerical localization of hidden attractor is demonstrated.

Mathematics::Dynamical SystemsChaoticLyapunov exponentsymbols.namesakeAttractorSelf-excited attractorHidden attractorHomoclinic orbitCoexistence of attractorsMultistabilityMathematicsHomoclinic orbitRössler attractorNumerical AnalysisApplied Mathematicsta111Mathematical analysisLorenz-like systemMultistabilityLorenz systemNonlinear Sciences::Chaotic DynamicsClassical mechanicsModeling and SimulationLyapunov dimensionsymbolsLyapunov exponentCrisisCommunications in Nonlinear Science and Numerical Simulation
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Time-delay control for stabilization of the Shapovalov mid-size firm model

2020

Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control methods allows improvements in forecasting the dynamics of unstable economic processes and offers opportunities for governments, central banks, and other policy makers to modify the behaviour of the economic system to achieve its best performance. One effective method for control of chaos and computation of unstable periodic orbits (UPOs) is the unstable delay feedback control (UDFC) approach, suggested by K. Pyragas. This paper proposes the application of the Pyragas' me…

kaaosteoriaFOS: Physical sciencesLorenz-like systemtaloudelliset ennusteetunstable periodic orbitNonlinear Sciences - Chaotic Dynamicsmid-size firm modelvakauttaminen (talous ja yhteiskunta)stabilizationNonlinear Sciences::Chaotic Dynamicsnonlinear dynamicssäätöteoriachaotic economytime-delay feedback controltaloudelliset mallitcontrol of chaosChaotic Dynamics (nlin.CD)dynaamiset systeemit
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Localization and dimension estimation of attractors in the Glukhovsky-Dolzhansky system

2016

lämmön kuljetuskaaosteorianumeeriset menetelmätLyapunov exponentsLorenz-like systemattraktoritGlukhovsky-Dolzhansky systemchaotic attractorLyapunov dimensionfluiditdynaamiset systeemitmatemaattiset mallitdifferentiaaliyhtälöthidden attractor
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