Sub-Hopf/fold-cycle bursting and its relation to (quasi-)periodic oscillations

摘要: We investigate the emergence of bursting oscillations and their relation to (quasi-) periodic behaviour in two different model systems, a pH oscillator calcium oscillator. Both systems are described by 3-dimensional ODE follow 'routes' as parameters varied. In first part, we exploit slow-fast structure show that sub-Hopf/fold-cycle type over wide range parameters. For this purpose, slow variable is used quasi-static bifurcation parameter for remaining 2-dimensional fast subsystem. oscillator, subsequent two-parameter continuation reveals transition from fold/sub-Hopf type. second argue particular constellation subcritical Hopf together with saddle-node orbit (fold-cycle) may not only account oscillations, but also allows (quasi-)periodic on 2-torus suggesting common origin both types dynamics.