Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

doi:10.1088/1674-1056/acc8c4

中国物理B ›› 2023, Vol. 32 ›› Issue (9): 90503-090503.doi: 10.1088/1674-1056/acc8c4

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Peng-Chong Zhao(赵鹏翀)^1,2, Hao-Juan Wei(卫皓娟)³, Zhen-Kun Xu(徐振坤)^1,2, Di-Yi Chen(陈帝伊)^1,2,†, Bei-Bei Xu(许贝贝)^1,2, and Yu-Meng Wang(王雨萌)^1,2

1 Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest Agriculture and Forestry University, Yangling 712100, China;
2 Institute of Water Resources and Hydropower Research, Northwest Agriculture and Forestry University, Yangling 712100, China;
3 Dongfang Electric Machinery Co Ltd, Deyang 618000, China

收稿日期:2023-02-15 修回日期:2023-03-27 接受日期:2023-03-30 发布日期:2023-09-01
通讯作者: Di-Yi Chen E-mail:diyichen@nwsuaf.edu.cn
基金资助:
Project supported by the Fundamental Research Funds for the Northwest A & F University (Grant No. /Z1090220172), the Scientific Research Foundation of the Natural Science Foundation of Shaanxi Province, China (Grant No. 2019JLP- 24), the Shaanxi Province Innovation Talent Promotion PlanScience and Technology Innovation Team, China (Grant No. 2020TD-025), and the Water Conservancy Science and Technology Program of Shaanxi Province, China (Grant No. 2018slkj-9).

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Peng-Chong Zhao(赵鹏翀)^1,2, Hao-Juan Wei(卫皓娟)³, Zhen-Kun Xu(徐振坤)^1,2, Di-Yi Chen(陈帝伊)^1,2,†, Bei-Bei Xu(许贝贝)^1,2, and Yu-Meng Wang(王雨萌)^1,2

1 Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest Agriculture and Forestry University, Yangling 712100, China;
2 Institute of Water Resources and Hydropower Research, Northwest Agriculture and Forestry University, Yangling 712100, China;
3 Dongfang Electric Machinery Co Ltd, Deyang 618000, China

Received:2023-02-15 Revised:2023-03-27 Accepted:2023-03-30 Published:2023-09-01
Contact: Di-Yi Chen E-mail:diyichen@nwsuaf.edu.cn
Supported by:
Project supported by the Fundamental Research Funds for the Northwest A & F University (Grant No. /Z1090220172), the Scientific Research Foundation of the Natural Science Foundation of Shaanxi Province, China (Grant No. 2019JLP- 24), the Shaanxi Province Innovation Talent Promotion PlanScience and Technology Innovation Team, China (Grant No. 2020TD-025), and the Water Conservancy Science and Technology Program of Shaanxi Province, China (Grant No. 2018slkj-9).

摘要/Abstract

摘要： This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link, and propose a new six-dimensional system, which exhibits some hidden attractors. The parameter switching algorithm is used to numerically study the dynamic behaviors of the system. Moreover, it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors. A self-excited attractor with the change of its parameters is also recognized. In addition, numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra, Lyapunov dimensions, bifurcation diagrams, phase space orbits, and basins of attraction. Consequently, the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable. These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems, and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.

关键词: nonlinear hydro-turbine governing systems, hidden attractors, basin of attraction, Lyapunov exponent spectrum

Abstract: This work studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link, and propose a new six-dimensional system, which exhibits some hidden attractors. The parameter switching algorithm is used to numerically study the dynamic behaviors of the system. Moreover, it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors. A self-excited attractor with the change of its parameters is also recognized. In addition, numerical simulations are carried out to analyze the dynamic behaviors of the proposed system by using the Lyapunov exponent spectra, Lyapunov dimensions, bifurcation diagrams, phase space orbits, and basins of attraction. Consequently, the findings in this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable. These simulation results are conducive to better understanding of hidden chaotic attractors in higher-dimensional dynamical systems, and are also of great significance in revealing chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes of initial values.

Key words: nonlinear hydro-turbine governing systems, hidden attractors, basin of attraction, Lyapunov exponent spectrum

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.-a (Nonlinear dynamics and chaos) 05.45.Pq (Numerical simulations of chaotic systems) 05.45.Df (Fractals)

Peng-Chong Zhao(赵鹏翀), Hao-Juan Wei(卫皓娟), Zhen-Kun Xu(徐振坤), Di-Yi Chen(陈帝伊), Bei-Bei Xu(许贝贝), and Yu-Meng Wang(王雨萌). Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis[J]. 中国物理B, 2023, 32(9): 90503-090503.

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Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

Existence of hidden attractors in nonlinear hydro-turbine governing systems and its stability analysis

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