Periodic flows to chaos based on discrete implicit mappings of continuous nonlinear systems

ACJ Luo - International Journal of Bifurcation and Chaos, 2015 - World Scientific
This paper presents a semi-analytical method for periodic flows in continuous nonlinear
dynamical systems. For the semi-analytical approach, differential equations of nonlinear …

On analytical routes to chaos in nonlinear systems

ACJ Luo - International Journal of Bifurcation and Chaos, 2014 - World Scientific
In this paper, the analytical methods for approximate solutions of periodic motions to chaos
in nonlinear dynamical systems are reviewed. Briefly discussed are the traditional analytical …

Multiple bifurcation trees of period-1 motions to chaos in a periodically forced, time-delayed, hardening Duffing oscillator

ACJ Luo, S Xing - Chaos, Solitons & Fractals, 2016 - Elsevier
In this paper, bifurcation trees of periodic motions in a periodically forced, time-delayed,
hardening Duffing oscillator are analytically predicted by a semi-analytical method. Such a …

Towards infinite bifurcation trees of period-1 motions to chaos in a time-delayed, twin-well Duffing oscillator

S Xing, ACJ Luo - Journal of Vibration Testing and …, 2017 - lhscientificpublishing.com
In this paper, bifurcation trees of periodic motions to chaos in a periodically forced, time-
delayed, twin-well Duffing oscillator are pre-dicted by a semi-analytical method. The twin …

Symmetric and asymmetric period-1 motions in a periodically forced, time-delayed, hardening Duffing oscillator

ACJ Luo, S Xing - Nonlinear dynamics, 2016 - Springer
In this paper, complex symmetric and asymmetric period-1 motions in a periodically forced,
time-delayed, hardening Duffing oscillator are predicted through an implicit discrete map …

Period-m motions to chaos in a periodically forced, Duffing oscillator with a time-delayed displacement

ACJ Luo, H Jin - International Journal of Bifurcation and Chaos, 2014 - World Scientific
In this paper, periodic motions in a periodically excited, Duffing oscillator with a time-delayed
displacement are investigated through the Fourier series, and the stability and bifurcation of …

Complex period-1 motions of a periodically forced Duffing oscillator with a time-delay feedback

ACJ Luo, H Jin - International Journal of Dynamics and Control, 2015 - Springer
In this paper, complex period-1 motions in a periodically forced Duffing oscillator with a time-
delay feedback are investigated, and the symmetric and asymmetric, complex period-1 …

Symmetric and asymmetric periodic motions of a nonlinear oscillator with a tuned mass damper inerter

C Guo, ACJ Luo - The European Physical Journal Special Topics, 2021 - Springer
In this paper, periodic responses in a nonlinear oscillator with electromagnetic resonant
shunt tuned mass damper inerter (ERS-TMDI) are studied. Symmetric and asymmetric …

On possible infinite bifurcation trees of period-3 motions to chaos in a time-delayed, twin-well Duffing oscillator

S Xing, ACJ Luo - International Journal of Dynamics and Control, 2018 - Springer
In this paper, bifurcation trees of period-3 motions to chaos in a periodically forced, time-
delayed, twin-well Duffing oscillator are investigated. Such period-3 motions and …

Periodic motions on bifurcation trees in an inverted pendulum with a periodically moving base

C Guo, ACJ Luo - International Journal of Dynamics and Control, 2021 - Springer
This paper studies periodic motions of an inverted pendulum with a periodically moving
base. A bifurcation tree of period-1 to period-8 motions is predicted through a discrete …