  We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally
coupled chaotic cubic maps in a bistability regime. In particular, we perform a
detailed study on the transition "coherence -- incoherence" for varying
coupling strength for a fixed interaction radius. For the 2D ensemble we show
the appearance of amplitude and phase chimera states previously reported for 1D
ensembles of nonlocally coupled chaotic systems. Moreover, we uncover a novel
type of chimera state, double-well chimera, which occurs due to the interplay
of the bistability of the local dynamics and the 2D ensemble structure.
Additionally, we find double-well chimera behaviour for steady states which we
call double-well chimera death. A distinguishing feature of chimera patterns
observed in the lattice is that they mainly combine clusters of different
chimera types: phase, amplitude and double-well chimeras.
