We show the existence and stability of frozen splay states as well as temporally chaotic splay states in a coupled sine circle map lattice system using analytic and numerical techniques. The splay states are observed for very low values of the nonlinearity parameter, i.e., for circle maps which deviate very slightly from the shift map case. We also observe that, depending on the parameters of the system, the splay states bifurcate to mixed or chimera splay states, consisting of a mixture of splay and synchronised states, together with kinks in the phases of some of the maps and then to a globally synchronised state. We estimate the parameter regions where these pure states and the mixed states are seen. We also briefly show that similar spatial splay structures can exist in experimentally realisable systems like Josephson junction arrays and Hartley-like oscillator arrays.

PACS Nos 12.60.Jv; 12.10.Dm; 98.80.Cq; 11.30.Hv