M. Golubitsky, K. Josic and L-J. Shiau
Bursting in coupled cell systems
In: Bursting: The Genesis of Rhythm in the Nervous System.
(S. Coombes and P.C. Bressloff, eds.)
World Scientific Publ. Co., 2005, 205-225.
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.