Investigation and analysis of the Lyapunov Control of Zohdy/Harb nonlinear oscillator

2017 ◽  
Author(s):  
Mohammed Alghassab ◽  
Mohamed A. Zohdy
Keyword(s):  
Nonlinear Oscillator ◽  
Lyapunov Control

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

Boosting the Output Performance of the Triboelectric Nanogenerator through the Nonlinear Oscillator

2021 ◽  
Vol 13 (5) ◽  
pp. 6331-6338
Author(s):  
Dong Guan ◽  
Guoqiang Xu ◽  
Xin Xia ◽  
Jiaqi Wang ◽  
Yunlong Zi
Keyword(s):  
Nonlinear Oscillator ◽  
Triboelectric Nanogenerator ◽  
Output Performance

Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator

2014 ◽  
Vol 24 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Fourier Series ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Series Solution ◽  
Parametric Oscillator ◽  
Periodic Motions ◽  
Parametric Oscillators ◽  
Harmonic Term ◽  
Nonlinear Behaviors

In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.

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