Bursting oscillations in a hydro-turbine governing system with two time scales<xref rid="cpb_26_12_128202fn1" ref-type="fn">*</xref> <fn id="cpb_26_12_128202fn1"> <label>*</label> <p>Project supported by the Scientific Research Foundation of the National Natural Science Foundation of China–Outstanding Youth Foundation (Grant No. 51622906), the National Natural Science Foundation of China (Grant No. 51479173), the Fundamental Research Funds for the Central Universities, China (Grant No. 201304030577), the Scientific Research Funds of Northwest A & F University, China (Grant No. 2013BSJJ095), the Science Fund for Excellent Young Scholars from Northwest A & F University (Grant No. Z109021515), and the Shaanxi Provincial Nova Program, China (Grant No. 2016KJXX-55).</p> </fn>

Bursting oscillations in a hydro-turbine governing system with two time scales* *

Project supported by the Scientific Research Foundation of the National Natural Science Foundation of China–Outstanding Youth Foundation (Grant No. 51622906), the National Natural Science Foundation of China (Grant No. 51479173), the Fundamental Research Funds for the Central Universities, China (Grant No. 201304030577), the Scientific Research Funds of Northwest A & F University, China (Grant No. 2013BSJJ095), the Science Fund for Excellent Young Scholars from Northwest A & F University (Grant No. Z109021515), and the Shaanxi Provincial Nova Program, China (Grant No. 2016KJXX-55).

Han Qing-Shuang¹, Chen Di-Yi^{1, 2, †}, Zhang Hao¹

(color online) Bifurcation diagrams of the mechanical torque m_t with respect to the governor parameter k_d: (a) bifurcation diagram of the autonomous HTGS with single time scale at 2.5 ≤ k_d ≤ 5.5; (b) local amplification of the bifurcation diagram of the autonomous HTGS with single time scale at 3.8 ≤ k_d ≤ 4.2; (c) bifurcation diagram of the non-autonomous HTGS with two time scales at 2.5 ≤ k_d ≤ 5.5; and (d) local amplification of the bifurcation diagram of the non-autonomous HTGS with two time scales at 3.8 ≤ k_d ≤ 4.2.