  We examine the steady state and dynamic behaviour of an optical resonator
comprised of two interlinked fibre loops sharing a common pump. A coupled Ikeda
map models with great accuracy the field evolution within and exchange between
both fibres over a single roundtrip. We find this supports a range of rich
multi-dimensional bistability in the continuous wave regime, as well as
previously unseen cavity soliton states. Floquet analysis reveals that
modulation and parametric instabilities occur over wider domains than in
single-fibre resonators, which can be tailored by controlling the relative
dispersion and resonance frequencies of the two fibre loops. Parametric
instability gives birth to train of pulses with a peculiar period-doubling
behavior.
