Bursting in Coupled Cell Systems

Periodic bursting in fast-slow systems can be viewed as closed paths through the unfolding parameters of degenerate singularities. Using this approach we show that bursting in coupled systems can have interesting behavior. We focus on two identical cell systems and use the $\Z_2$ symmetry present in such systems to illustrate interesting bursting phenomena. In particular, we show that Hopf/Hopf mode interactions can lead to bursting between in phase and out of phase periodic solutions and symmetry-breaking Takens-Bogdanov singularities can lead to bursting that randomly chooses between two (symmetrically related) limit cycles.

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