Hidden oscillations in dynamical systems. 16 Hilbert's problem, Aizerman's and Kalman's conjectures, hidden attractors in Chua's circuits

DOI10.1007/s10958-014-2017-6zbMath1338.37045OpenAlexW1965746978WikidataQ109649613 ScholiaQ109649613MaRDI QIDQ2259058

Nikolay V. Kuznetsov, Gennady Alekseevich Leonov

Publication date: 27 February 2015

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-014-2017-6

zbMATH Keywords

limit cycledynamical systemhidden oscillationchaotic hidden attractor

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Computational methods for bifurcation problems in dynamical systems (37M20)

Related Items (13)

Three-dimensional chaotic autonomous system with a circular equilibrium: analysis, circuit implementation and its fractional-order form ⋮ Simple Chaotic Flows with a Curve of Equilibria ⋮ The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors ⋮ A Tribute to J. C. Sprott ⋮ Hidden Attractor in a Passive Motion Model of Compass-Gait Robot ⋮ Are Perpetual Points Sufficient for Locating Hidden Attractors? ⋮ Constructing and analyzing of a unique three-dimensional chaotic autonomous system exhibiting three families of hidden attractors ⋮ Hidden attractors in dynamical systems ⋮ Categorizing Chaotic Flows from the Viewpoint of Fixed Points and Perpetual Points ⋮ Limitation of Perpetual Points for Confirming Conservation in Dynamical Systems ⋮ Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium ⋮ Method for constructing periodic solutions of a controlled dynamic system with a cylindrical phase space ⋮ A new chaotic system with equilibria located on a line and its circuit implementation

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