  The flow past inline oscillating rectangular cylinders is studied numerically
at a Reynolds number representative of two-dimensional flow. A symmetric mode,
known as S-II, consisting of a pair of oppositely-signed vortices on each side,
observed recently in experiments, is obtained computationally. A new symmetric
mode, named here as S-III, is also found. At low oscillation amplitudes, the
vortex shedding pattern transitions from antisymmetric to symmetric smoothly
via a regime of intermediate phase. At higher amplitudes, this intermediate
regime is chaotic. The finding of chaos extends and complements the recent work
of Perdikaris et al. [1]. Moreover it shows that the chaos results from a
competition between antisymmetric and symmetric shedding modes. Rectangular
cylinders rather than square are seen to facilitate these observations. A
global, and very reliable, measure is used to establish the existence of chaos.
