Phase transitions of extended-range probabilistic cellular automata with two absorbing states

We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by competing ferromagnetic linear and antiferromagnetic nonlinear couplings. Despite its simplicity, this model exhibits an extremely rich phase diagram. We present numerical results and mean-field approximations.