Hidden attractors in dynamical systems: From hidden oscillations in hilbert-kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in chua circuits

International Journal of Bifurcation and Chaos

Volumn 23, Issue 1, 2013, Pages

  Leonov, G A ^a   Kuznetsov, N V ^a,b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

16th Hilbert problem; absolute stability; Aizerman conjecture; Chua circuits; describing function method; drilling system; harmonic balance; hidden attractor; Hidden oscillation; induction motor; Kalman conjecture; large (normal amplitude) and small limit cycle; Lienard equation; Lyapunov focus values (Lyapunov quantities Poincar Lyapunov constants Lyapunov coefficients); nonlinear control system; phase locked loop (PLL); quadratic system

Indexed keywords

AIRCRAFT ACCIDENTS; AUTOMATION; CIRCUIT OSCILLATIONS; CONTROL SYSTEM STABILITY; CONTROL SYSTEMS; DELTA SIGMA MODULATION; DRILLING; DYNAMICAL SYSTEMS; EXCITED STATES; FIGHTER AIRCRAFT; FLIGHT CONTROL SYSTEMS; INDUCTION MOTORS; LOCKS (FASTENERS); NONLINEAR CONTROL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PHASE LOCKED LOOPS; PROCESS CONTROL; SYSTEM STABILITY; TIMING CIRCUITS;

ABSOLUTE STABILITY; AIZERMAN CONJECTURE; CHUA CIRCUIT; DESCRIBING FUNCTION METHODS; DRILLING SYSTEMS; HARMONIC BALANCE; HIDDEN ATTRACTOR; HIDDEN OSCILLATION; HILBERT PROBLEM; KALMAN CONJECTURE; LIENARD EQUATION; LIMIT-CYCLE; LYAPUNOV COEFFICIENT; PHASE LOCKED LOOP (PLL); QUADRATIC SYSTEMS;

PROBLEM SOLVING;

EID: 84874642094     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127413300024     Document Type: Review

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