Nonlinear fast–slow dynamics of a coupled fractional order hydropower generation system<xref rid="cpb_27_12_128202fn1" ref-type="fn">*</xref><fn id="cpb_27_12_128202fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China for Outstanding Youth (Grant No. 51622906), the National Natural Science Foundation of China (Grant No. 51479173), the Fundamental Research Funds for the Central Universities (Grant No. 201304030577), the Scientific Research Funds of Northwest A & F University (Grant No. 2013BSJJ095), and the Science Fund for Excellent Young Scholars from Northwest A & F University and Shaanxi Nova Program, China (Grant No. 2016KJXX-55).</p></fn>

Nonlinear fast–slow dynamics of a coupled fractional order hydropower generation system**

Project supported by the National Natural Science Foundation of China for Outstanding Youth (Grant No. 51622906), the National Natural Science Foundation of China (Grant No. 51479173), the Fundamental Research Funds for the Central Universities (Grant No. 201304030577), the Scientific Research Funds of Northwest A & F University (Grant No. 2013BSJJ095), and the Science Fund for Excellent Young Scholars from Northwest A & F University and Shaanxi Nova Program, China (Grant No. 2016KJXX-55).

Gao Xiang^{1, 2}, Chen Diyi^{1, 2, 3, †}, Zhang Hao^{1, 2}, Xu Beibei^{1, 2}, Wang Xiangyu³

(color online) The bifurcation diagrams of the rotational speed n with increase of the periodic excitation frequency Ω. (a) Ω from 0.01 to 1; (b) Ω from 0.01 to 0.1; (c) Ω from 0.05 to 0.2; (d) Ω from 0.2 to 0.5; (e) Ω from 0.5 to 1; (f) Ω from 1 to 5.