图 10  (H, T, V ) 空间中CB的双参分岔和相轨迹. 蓝色、黄色和粉色面分别由不稳定焦点、鞍点和稳定结点构成, 红色、绿色、黑色粗线分别代表鞍结 (SN) 分岔、不变环上的鞍结 (SNIC) 分岔和超临界霍普夫 (SupHopf) 分岔, 上、下绿面代表稳定极限环的极大值 ($ {V_{{\max}}} $) 和极小值 ($ {V_{{\min}}} $), 黑色细线代表簇的相轨迹　(a) 全图; (b) 图(a)中B点附近的放大图, B点位于SupHopf分岔曲线正下方, 对应簇的结束相位; (c) 图(a)中BT分岔点附近的放大; (d) 图(a)中A点和C点附近的放大, A点在SNIC分岔曲线正下方, 对应CB轨迹的起始相位, C点距离SN分岔曲线较远

Fig. 10.  Two-parameter bifurcation of fast system and phase trajectory of CB in the (H, T, V ) space. The blue, yellow, and pink surfaces are composed of the unstable focus, the saddle and the stable node, respectively. The red, green, and black thick curves represent the saddle-node (SN) bifurcation, the saddle-node on invariant circle (SNIC) bifurcation, and the supercritical Andronov-Hopf (SupHopf) bifurcation. The upper and lower green surfaces represent the maximum value ($ {V_{{\max}}} $) and the minimum value ($ {V_{{\min}}} $) of the stable limit cycle, respectively, and the black thin curve represents the phase trajectory of the bursting: (a) Global view; (b) the enlargement near point B in Fig. (a), point B is located just below the SupHopf bifurcation curve, corresponding to the termination phase of the burst; (c) the enlargement near BT bifurcation point in Fig. (a); (d) the enlargement near points A and C in Fig. (a). The point A is just below the SNIC bifurcation curve, corresponding to the start phase of burst, and point C is far from the SN bifurcation curve.