Open AccessBook
Continuous Dynamical Systems
Albert C. J. Luo,Carlo Mariconda +1 more
- 01 Jan 2012
63
TL;DR: Continuous Dynamical Systems as mentioned in this paper provides a simple and concise view of a theory of stability and bifurcation in continuous dynamical systems for a better understanding of regularity and complexity in dynamic systems.
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Abstract: Continuous Dynamical Systems is a unique book on chaos which can be analytically expressed rather than numerically simulated only, and provides a simple and concise view of a theory of stability and bifurcation in continuous dynamical systems for a better understanding of regularity and complexity in dynamical systems. Linear continuous systems with repeated eigenvalues are presented as an introduction. Higher-order singularity, stability and bifurcation in nonlinear
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Citations
Analytical solutions for asymmetric periodic motions to chaos in a hardening Duffing oscillator
Albert C. J. Luo,Jianzhe Huang +1 more
TL;DR: In this paper, the analytical dynamics of asymmetric periodic motions in the periodically forced, hardening Duffing oscillator via the generalized harmonic balance method was investigated, and the bifurcation trees from asymmetric period-1 motions to chaos were presented.
50
Bifurcation of periodic orbits emanated from a vertex in discontinuous planar systems
Nan Hu,Zhengdong Du +1 more
TL;DR: The maximum number of limit cycles bifurcate from the periodic annulus can be affected by the position of the switching lines and this work generalizes to systems with discontinuities on finitely many smooth curves.
39
On bifurcation trees of period-1 to period-2 motions in a nonlinear Jeffcott rotor system
TL;DR: In this article, the bifurcation trees of different period-1 to period-2 motion are presented, and there are many segments for different periods of 1 and 2 motions.
38
Multiple bifurcation trees of period-1 motions to chaos in a periodically forced, time-delayed, hardening Duffing oscillator
Albert C. J. Luo,Siyuan Xing +1 more
TL;DR: In this article, a semi-analytical method is proposed to predict periodic motions in a periodically forced, time-delayed, hardening Duffing oscillator, based on the differential equation discretization of a nonlinear dynamical system.
34
Analytical solutions for periodic motions to chaos in nonlinear systems with/without time-delay
TL;DR: In this paper, the analytical solutions of periodic flows to chaos for time-delayed, nonlinear systems with/without periodic excitations are presented, and time delayed, non-linear vibra- tion systems are also discussed.