Coupling and noise induced spiking-bursting transition in a parabolic bursting model

The transition from tonic spiking to bursting is an important dynamic process that carry physiologically relevant information. In this work, coupling and noise induced spiking-bursting transition is investigated in a parabolic bursting model with specific discussion on their cooperation effects. Fast/slow analysis shows that weak coupling may help to induce the bursting by changing the geometric property of the fast subsystem so that the original unstable periodical solution are stabilized. It turned out that noise can play the similar stabilization role and induce bursting at appropriate moderate intensity. However, their cooperation may either strengthen or weaken the overall effect depending on the choice of noise level.