Fractal structures in centrifugal flywheel governor system

Rao, Xiao-Bo; Chu, Yan-Dong; Lu-Xu,; Chang, Yunlong; Zhang, Jiangang

doi:10.1016/j.cnsns.2017.03.016

Cited by 35 publications

(13 citation statements)

References 41 publications

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“…This work reported sets of high-resolution stability diagrams for parameter windows around recently studied experimental values. 6 By classifying the spikes per period 37,[42][43][44][45][46][47][48] of the sustained periodic oscillations, stability diagrams were computed both for the galvanostatic and for the potentiostatic control modes.…”

Section: Discussionmentioning

confidence: 99%

Phase diagrams and dynamical evolution of the triple-pathway electro-oxidation of formic acid on platinum

Freire

Calderón-Cárdenas

Varela

et al. 2020

Phys. Chem. Chem. Phys.

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Section: Discussionmentioning

confidence: 99%

Phase diagrams and dynamical evolution of the triple-pathway electro-oxidation of formic acid on platinum

Freire

Calderón-Cárdenas

Varela

et al. 2020

Phys. Chem. Chem. Phys.

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“…From Fig. 2(a), we can clearly see that there are many symmetric structures, Arnold's tongues structures [37] (which are caused by Neimark-Sacker bifurcation) and V-shape islands [38]…”

Section: The Path To Chaosmentioning

confidence: 99%

Complex dynamical behaviors in a Bertrand game with service factor and differentiated products

Zhou

2021

Nonlinear Dyn

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In this paper, taking the factor of service level provided by the manufacturers into consideration, a static duopolistic Bertrand game with service factor is studied first, in which these two oligarchs produce differentiated products. A dynamic game model of duopoly Bertrand with boundedly rational is established with using the gradient mechanism. By using numerical simulation tools, there are two paths for the system to drop into chaos, that is, flip bifurcation and Neimark-Sacker bifurcation. The symmetric structures can be found from two-parameter bifurcation diagrams. Saddle-homoclinic bifurcation also can be observed from the evolution process of phase portraits. In addition, the emergence of intermittent chaos implies that the established system has the capability of self-regulating, where PM-I intermittency, PM-III intermittency and crisis-induced intermittency have been studied. With the help of the critical curves, the qualitative changes on the basin of attraction are investigated. At last, it can be found that the values of product differentiation degree and service spillover effect are not the bigger the better. Keeping these two parameters in a relatively small range will be conducive to the long-term stable operation of the two manufacturers.

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“…Owing to the simple yet effective characteristics, the centrifugal governor devices have been widely used in many rotating machines to avoid potential damage, such as in the internal combustion engines, fueled turbines, modern striking clocks and so on. Induced by the inherent nonlinearities, many dynamical phenomena have been observed and reported in such systems, including periodic oscillations [28,29], chaotic motions [30,31], hyperchaotic behavior [32], multistability [15,33], fractal and mode-locking structures [34,35]. To avoid the damages caused by the undesired system response, various control schemes have been proposed to stabilize the system.…”

Section: Introductionmentioning

confidence: 99%

Two-Parameter Dynamics of An Autonomous Mechanical Governor System With Time Delay

Deng

Wen

et al. 2021

Preprint

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Understanding of dynamical behavior in the parameter-state space plays a vital role in the optimal design and motion control of mechanical governor systems. By combining the GPU parallel computing technique with two determinate indicators, namely, the Lyapunov exponents and Poincaré section, this paper presents a detailed study on the two-parameter dynamics of a mechanical governor system with different time delays. By identifying different system responses in two-parameter plane, it is shown that the complexity of evolutionary process can increase significantly with the increase of time delay. The path-following strategy and the time domain collocation method are used to explore the details of the evolutionary process. An interesting phenomenon is found in the dynamical behavior of the delayed governor system, which can cause the inconsistency between the number of intersection points of certain periodic response on Poincaré section and the actual period characteristic. For example, the commonly exhibited period-1 orbit may have two or more intersection points on the Poincaré section instead of one point. Furthermore, the variations of basins of attraction are also discussed in the plane of initial history conditions to demonstrate the observed multistability phenomena and chaotic transitions.

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Fractal structures in centrifugal flywheel governor system

Cited by 35 publications

References 41 publications

Phase diagrams and dynamical evolution of the triple-pathway electro-oxidation of formic acid on platinum

Phase diagrams and dynamical evolution of the triple-pathway electro-oxidation of formic acid on platinum

Complex dynamical behaviors in a Bertrand game with service factor and differentiated products

Two-Parameter Dynamics of An Autonomous Mechanical Governor System With Time Delay

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