Institute for Mathematics and Its Applications
Edgar Knobloch, University of California Berkeley
The interaction of two unstable oscillatory modes of opposite parity can produce periodic or irregular bursting close to threshold (A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579, 1996). These bursts take the form of large amplitude events separated by long periods of stasis. This talk will describe joint work with Jeff Moehlis to understand the essence of this behavior using the Hopf bifurcation with broken D4 symmetry. The bursts are found to be associated with global bifurcations involving fixed points and limit cycles ``at infinity''. This approach allows us to identify the conditions for the presence of repeated bursts and to elucidate the origin of chaotic bursting. The results enable us to interpret experiments on the so-called ``repeated transients'' observed in binary fluid convection.