Local instability and localization of attractors. From stochastic generator to Chua's systems

DOI10.1007/BF00992721zbMath0826.58020OpenAlexW2046472465MaRDI QIDQ1897647

D. V. Ponomarenko, V. B. Smirnova, Gennady Alekseevich Leonov

Publication date: 22 November 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00992721

zbMATH Keywords

instabilitychaosLyapunov functionLyapunov stabilitystrange attractororbital stabilityZhukovskij stabilityLyapunov characteristic exponentnonlocal reduction methodpositive invariant setfrequency-domain theoremsystem in variations

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Stability theory for smooth dynamical systems (37C75)

Related Items (18)

Method of ``transition into space of derivatives: 40 years of evolution ⋮ Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part ⋮ The asymptotic rigidity of a compact invariant set of a dynamic system stable in the Poisson sense ⋮ Zhukovskij quasi-stable orbits of impulsive dynamical systems ⋮ Review on contraction analysis and computation of contraction metrics ⋮ Transverse contraction criteria for existence, stability, and robustness of a limit cycle ⋮ Can state feedback stabilize a chaotic orbit uniformly and asymptotically in the sense of orbital stability? ⋮ On limiting properties of Lyapunov asymptotically stable and Zhukovsky asymptotically rigid trajectories of a dynamic system ⋮ Necessary conditions for a limit cycle and its basin of attraction. ⋮ New results of the ultimate bound on the trajectories of the family of the Lorenz systems ⋮ The limit sets of uniformly asymptotically Zhukovskij stable orbits ⋮ Asymptotic orbital stability conditions for flows by estimates of singular values of the linearization ⋮ Remarks on three types of asymptotic stability ⋮ Lyapunov asymptotic stability and Zhukovskij asymptotic stability ⋮ Orbital stabilization of point-to-point maneuvers in underactuated mechanical systems ⋮ On the new results of global exponential attractive set ⋮ The global structure of uniformly asymptotically Zhukovskiĭstable systems ⋮ Unnamed Item

Cites Work

• Stability by Liapunov's direct method. With applications
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• On the concept of attractor
• The structure of a strange attractor
• Strange attractors
• Stability theory by Liapunov's direct method
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Differential equations: Stability, oscillations, time lags
• On the stability of integral manifolds of functional differential equations
• On the existence and stability of the periodic solution of the second kind of a certain mechanical system
• A chaotic attractor from Chua's circuit
• Canonical realization of Chua's circuit family
• Strange attractors and chaotic motions of dynamical systems
• Roads to turbulence in dissipative dynamical systems
• The double scroll
• The double scroll family
• The dual double scroll equation
• Attraktorlokalisierung des Lorenz-Systems
• On Global Asymptotic Stability of Solutions of Differential Equations
• LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL
• Deterministic Nonperiodic Flow
• GLOBAL BIFURCATION ANALYSIS OF THE DOUBLE SCROLL CIRCUIT
• On the theory of optimum control
• Zur Eingrenzung des Lorenz‐Attraktors durch die Anwendung der nichtlokalen Reduktionsmethode und mit Hilfe von Vergleichssystemen zweiter Ordnung
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Local instability and localization of attractors. From stochastic generator to Chua's systems