Fig. 1. Typical compound relaxation oscillations in system (1): (a) ; (b) ; (c) . Other parameters are fixed at , , , , and .

Fig. 2. Bifurcation sets of the subsystem (2a) (a) and (2b) (b) in the parameter plane . Here GH represent the generalized Hopf bifurcation, SubH represent the subcritical Hopf bifurcation, SupH represent the supercritical Hopf bifurcation, LPC represent the limit point cycle bifurcation. The values of system parameters are the same as those in Fig. 1.

Fig. 3. Typical stability and bifurcation behaviors of the fast subsystem (2) in the areas A, B and C: (a1), (a2) ; (b1), (b2) ; (c1), (c2) . The values of other parameters are the same as those in Fig. 1.

Fig. 4. Bifurcation sets of the subsystem (2b) in the parameter plane . The values of other parameters are the same as those in Fig. 1(a).

Fig. 5. Bifurcation diagrams of the subsystem (2b): (a) 1.1; (b) . The values of other parameters are the same as those in Fig. 1(a).

Fig. 6. Fast-slow analysis of the relaxation oscillations in Fig. 1(a): (a) Overlay of the transformed phase diagram of the relaxation oscillations and the bifurcation diagram in Fig. 3(a1) (related to the subsystem (2a)); (b) overlay of the transformed phase diagram of the relaxation oscillations and the bifurcation diagram in Fig. 3(a2) (related to the subsystem (2b)); (c) a whole period of the relaxation oscillations. Here and other parameters are the same as those in Fig. 1.

Fig. 7. Fast-slow analysis of the relaxation oscillations in Fig. 1(b).

Fig. 8. Fast-slow analysis of the relaxation oscillations in Fig. 1(c).