Noise induced escape from a nonhyperbolic chaotic attractor of a periodically driven nonlinear oscillator

2016 ◽  
Vol 26 (6) ◽  
pp. 063112 ◽  
Author(s):  
Zhen Chen ◽  
Yang Li ◽  
Xianbin Liu
Keyword(s):  
Chaotic Attractor ◽  
Nonlinear Oscillator ◽  
Periodically Driven

Features of a chaotic attractor in a quasiperiodically driven nonlinear oscillator

2021 ◽  
Vol 31 (7) ◽  
pp. 073118
Author(s):  
V. P. Kruglov ◽  
D. A. Krylosova ◽  
I. R. Sataev ◽  
E. P. Seleznev ◽  
N. V. Stankevich
Keyword(s):  
Chaotic Attractor ◽  
Nonlinear Oscillator

Bifurcation Analysis of Zero-Dispersion Nonlinear Resonance

1998 ◽  
Vol 08 (04) ◽  
pp. 701-712 ◽  
Author(s):  
R. Mannella ◽  
S. M. Soskin ◽  
P. V. E. McClintock
Keyword(s):  
Bifurcation Analysis ◽  
Nonlinear Oscillator ◽  
Nonlinear Resonance ◽  
External Noise ◽  
Periodically Driven ◽  
Onset Of Chaos

The problem of zero-dispersion nonlinear resonance — a phenomenon that can occur in a periodically-driven nonlinear oscillator whose eigenfrequency as a function of energy possesses an extremum — has been formulated in general for both the dissipative and nondissipative situations. A complete bifurcation analysis and classification of period-1 orbits is presented. The significance of bifurcations for the onset of chaos in the system, and for fluctuations in the presence of external noise, is discussed.

scholarly journals Fluctuational transitions and critical phenomena in a periodically driven nonlinear oscillator subject to weak noise

1993 ◽  
Author(s):  
M. I. Dykman ◽  
R. Mannella ◽  
D. G. Luchinsky ◽  
P. V. E. McClintock ◽  
N. D. Stein ◽  
...  
Keyword(s):  
Critical Phenomena ◽  
Nonlinear Oscillator ◽  
Weak Noise ◽  
Periodically Driven

scholarly journals PULSATING FEEDBACK CONTROL FOR STABILIZING UNSTABLE PERIODIC ORBITS IN A NONLINEAR OSCILLATOR WITH A NONSYMMETRIC POTENTIAL

2007 ◽  
Vol 17 (08) ◽  
pp. 2797-2803 ◽  
Author(s):  
G. LITAK ◽  
M. ALI ◽  
L. M. SAHA
Keyword(s):  
Feedback Control ◽  
Periodic Orbits ◽  
Efficient Method ◽  
Chaotic Attractor ◽  
Nonlinear Oscillator ◽  
Chaos Control ◽  
Degree Of Freedom ◽  
Unstable Periodic Orbits ◽  
Periodic State

We examine a strange chaotic attractor and its unstable periodic orbits in case of one-degree of freedom nonlinear oscillator with nonsymmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsating feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.

scholarly journals Random perturbations of a periodically driven nonlinear oscillator: escape from a resonance zone

Nonlinearity ◽  
2017 ◽  
Vol 30 (4) ◽  
pp. 1376-1404 ◽  
Author(s):  
Nishanth Lingala ◽  
N Sri Namachchivaya ◽  
Ilya Pavlyukevich
Keyword(s):  
Nonlinear Oscillator ◽  
Random Perturbations ◽  
Resonance Zone ◽  
Periodically Driven

Transport of quantum states of periodically driven systems

1990 ◽  
Vol 51 (8) ◽  
pp. 709-722 ◽  
Author(s):  
H.P. Breuer ◽  
K. Dietz ◽  
M. Holthaus
Keyword(s):  
Quantum States ◽  
Driven Systems ◽  
Periodically Driven
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