On symmetry-breaking bifurcation in the periodic parameter-switching Lorenz oscillator

Zhang, Chun; Han, Xiujing; Bi, Qinsheng

doi:10.1007/s11431-013-5301-7

Cited by 6 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is the set of folding parameters corresponding to the non-persistent bifurcation diagram of the universal unfolding G(a, µ, λ). The sets of bifurcation point, lag point, and double limit point correspond to the three types of the non-persistence bifurcation diagram [52,53].…”

Section: Analysis Of Bifurcation Characteristicmentioning

confidence: 99%

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

et al. 2019

View full text Add to dashboard Cite

As the core control system of a rolling mill, the hydraulic automatic gauge control (HAGC) system is key to ensuring a rolling process with high speed, high precision and high reliability. However, a HAGC system is typically a mechanical-electric-hydraulic coupling system with nonlinear characteristics. The vertical vibration of the load easily occurs during the working process, which seriously affects the stability of the system and the causes are difficult to determine. In this work, the theory and method of nonlinear dynamics were employed. The load vertical vibration model of the HAGC system was established. Then, the multi-scale method was utilized to solve the obtained model, and the singularity theory was further applied to derive the transition set. Moreover, the research object of this article focused on some nonlinear factors such as excitation force, elastic force and damping force. The effects of the above feature parameters on bifurcation behavior were emphatically explored. The bifurcation characteristic of the load vertical vibration of the HAGC system was revealed. The research results indicate that the bifurcation curves in each sub-region, divided by the transition set, possess their own topological structure. The changes of the feature parameters, such as the nonlinear stiffness coefficient, liquid column height, nonlinear damping coefficient, and external excitation have an influence on the vibration amplitude of the HAGC system. By reasonably adjusting the nonlinear stiffness coefficient to effectively avoid the resonance region, the stability of the system will be facilitated. Furthermore, this is conducive to the system’s stability as it properly controls the size of the liquid column height of the hydraulic cylinder. The appropriate nonlinear damping coefficient can decrease the unstable area, which is beneficial to the stability of the system. However, large external excitation is not conducive to the stability of the system.

show abstract

Section: Analysis Of Bifurcation Characteristicmentioning

confidence: 99%

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

et al. 2019

View full text Add to dashboard Cite

show abstract

“…However, many problems such as dynamical behaviors, bifurcations associated with the switching conditions, and the mechanism of complexity with the variation in the parameters are seldom researched. Switched systems introduce many new characteristics, especially strong nonlinearity and singularity caused by the non-differentiability or discontinuity of vector fields [22,23]. Therefore, many dynamic characteristics of nonsmooth systems can not be treated by the ordinary smooth dynamic system theory, and special theories and methods need to be developed.…”

Section: Introductionmentioning

confidence: 99%

Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators

2022

Self Cite

View full text Add to dashboard Cite

By introducing a switching scheme related to the state and time, a typical switched model alternating between a Duffing oscillator and van der Pol oscillator is established to explore the typical dynamical behaviors as well as the mechanism of the switched system. Shooting methods to locate the limit cycle and specify bifurcation sets are described by defining an appropriate Poincaré map. Different types of multiple-Focus/Cycle and single-Focus/Cycle period oscillations in the system can be observed. Symmetry-breaking, period-doubling, and grazing bifurcation curves are obtained in the plane of bifurcation parameters, dividing the parameters plane into several regions corresponding to different kinds of oscillations. Meanwhile, based on the numerical simulation and bifurcation analysis, the mechanisms of several typical dynamical behaviors observed in different regions are presented.

show abstract

Complicated behaviors and bifurcation mechanism of the periodic parameter-switching Chen system

Zhang

Han

2017

Optik

View full text Add to dashboard Cite

On symmetry-breaking bifurcation in the periodic parameter-switching Lorenz oscillator

Cited by 6 publications

References 27 publications

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

Bifurcation Characteristic Research on the Load Vertical Vibration of a Hydraulic Automatic Gauge Control System

Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators

Complicated behaviors and bifurcation mechanism of the periodic parameter-switching Chen system

Contact Info

Product

Resources

About