HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS (Q3401494): Difference between revisions

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English	HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS	scientific article

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scholarly article

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HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS (English)

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Zdzislaw E. Musielak

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publication date

30 January 2010

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zbMATH Keywords

high-dimensional chaos

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dissipative and driven nonlinear dynamical systems

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chaos control and synchronization

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MaRDI profile type

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Routes to chaos in high-dimensional dynamical systems: a qualitative numerical study

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Control of chaos: methods and applications. I: Methods

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Routes to chaos and turbulence. A computational introduction

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Writing the history of dynamical systems and chaos: `Longue durée' and revolution, disciplines and cultures

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Controlling chaos in high dimensional systems

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Chaotic Scenario in the Stenflo Equations

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Suppression of chaos in averaged oscillator driven by external and parametric excitations

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The dynamics of the Hénon map

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Experimental study of chaos in a driven pendulum

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Lyapunov exponents from observed time series

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NEW 3D-SCROLL ATTRACTORS IN HYPERCHAOTIC CHUA'S CIRCUITS FORMING A RING

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Cascading synchronized chaotic systems

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ON A GENERALIZED LORENZ CANONICAL FORM OF CHAOTIC SYSTEMS

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YET ANOTHER CHAOTIC ATTRACTOR

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On the relation between Rayleigh-Bénard convection and Lorenz system

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The double scroll family

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Canonical realization of Chua's circuit family

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LOCAL ACTIVITY IS THE ORIGIN OF COMPLEXITY

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A generalized Lorenz system

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Bounded Solutions of Finite Dimensional Approximations to the Boussinesq Equations

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Control and synchronization of chaos in high dimensional systems: Review of some recent results

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Roads to turbulence in dissipative dynamical systems

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Ergodic theory of chaos and strange attractors

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Synchronization of van der Pol oscillator and Chen chaotic dynamical system

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Quantitative universality for a class of nonlinear transformations

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The universal metric properties of nonlinear transformations

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Some characterizations of strange sets

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Comparison of different methods for computing Lyapunov exponents.

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Topological analysis of chaotic dynamical systems

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PHASE SYNCHRONIZATION AND CHAOS SUPPRESSION IN A SET OF TWO COUPLED NONLINEAR OSCILLATORS

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Crises, sudden changes in chaotic attractors, and transient chaos

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Attractors on an N-torus: Quasiperiodicity versus chaos

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Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics

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Nonlinear chaos control in a permanent magnet reluctance machine

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Chaos control of third-order phase-locked loops using backstepping nonlinear controller

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BIFURCATION TO HIGH-DIMENSIONAL CHAOS

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Dynamics and control of initialized fractional-order systems

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Analysing the chaotic motion of a driven pendulum

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Numerical study of quadratic area-preserving mappings

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A two-dimensional mapping with a strange attractor

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Second order averaging and bifurcations to subharmonics in duffing's equation

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A nonlinear oscillator with a strange attractor

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Large-scale flow in turbulent convection: a mathematical model

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Overview of coupled map lattices

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Peeling the onion of order and chaos in a high-dimensional Hamiltonian system

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On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection.

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Controlling chaotic oscillators without feedback

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HYPERCHAOTIC ATTRACTORS OF UNIDIRECTIONALLY-COUPLED CHUA’S CIRCUITS

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Bifurcation structure of two coupled periodically driven double-well Duffing oscillators.

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Generalizations of the concept of marginal synchronization of chaos

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Low-dimensional chaos in high-dimensional phase space: How does it occur?

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Controlling chaotic and hyperchaotic systems via energy regulation.

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Hyperchaos evolved from the generalized Lorenz equation

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A new chaotic attractor

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Deterministic Nonperiodic Flow

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A unified chaotic system with continuous periodic switch

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A NEW CHAOTIC ATTRACTOR COINED

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A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM

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Strange attractors and chaos control in periodically forced complex Duffing's oscillators

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A chaotic attractor from Chua's circuit

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Simple mathematical models with very complicated dynamics

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Bifurcation analysis of a new Lorenz-like chaotic system

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Integrable Duffing's maps and solutions of the Duffing equation

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Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom

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Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)

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Strange attractors and chaotic motions of dynamical systems

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Controlling chaos

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Silnikov's orbit in coupled Duffing's systems

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Synchronization in chaotic systems

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Pseudoperiodic driving: Eliminating multiple domains of attraction using chaos

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Fundamentals of synchronization in chaotic systems, concepts, and applications

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On a four-dimensional chaotic system

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Chaos control by nonfeedback methods in the presence of noise

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A nine-dimensional Lorenz system to study high-dimensional chaos

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Controlling chaotic dynamical systems

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An equation for continuous chaos

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An equation for hyperchaos

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Generalized Lorenz models and their routes to chaos. II: Energy-conserving horizontal mode truncations

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Generalized Lorenz models and their routes to chaos. I: Energy-conserving vertical mode truncations

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Generalized Lorenz models and their routes to chaos. III: Energy-conserving horizontal and vertical mode truncations

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On the nature of turbulence

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Bifurcation schemes of the Lorenz model

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A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

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Differentiable dynamical systems

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WHEN TWO COUPLED PENDULUMS EQUAL ONE: A SYNCHRONIZATION MACHINE

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Doubling bifurcations of destroyed \(\mathbb{T}^ 2\) tori

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Modelling chaos and hyperchaos with 3-D maps

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HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT

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Energy-conserving truncations for convection with shear flow

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Energy-conserving low-order models for three-dimensional Rayleigh-Bénard convection

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Energy conserving Galerkin approximations for 2-D hydrodynamic and MHD Bénard convection

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Lyapunov exponents for the Miles' spherical pendulum equations

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A generalized perturbed pendulum.

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The Lorenz attractor exists

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Survey of regular and chaotic phenomena in the forced Duffing oscillator

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Chaos control in Duffing system

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Determining Lyapunov exponents from a time series

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Chaos in the fractional order unified system and its synchronization

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On a complex Duffing system with random excitation

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Chaos-hyperchaos transition in coupled Rössler systems

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Transition to chaos for random dynamical systems

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Fractal distribution of floaters on a fluid surface and the transition to chaos for random maps

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A history of chemical oscillations and waves

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Controlling and tracking hyperchaotic Rössler system via active backstepping design

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Bifurcation behavior of the generalized Lorenz equations at large rotation numbers

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International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

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Identifiers

zbMATH Open document ID

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10.1142/S0218127409024517

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:3401494

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