We introduce and study coupled map lattices with complex state variable. The dynamical regimes of the finite-length systems are classified naturally in terms of a topological invariant – the overall phase shift accumulated along the whole length at fixed time. A stability analysis of the...

We discuss the so-called tricritical points at the border of the period-doubling transition to chaos and examine to what extent the associated universality applies to 2D dissipative maps. As a concrete example, the Ikeda map is studied together with its 1D analog. For the approximate 1D map, the...