Absorbing phase transitions of unidirectionally coupled nonequilibrium systems

We investigate the change of critical behavior of two-level hierarchy systems in which the second level (B) is unidirectionally coupled to the first (A) by the coupling dynamics A --> A + nB with n = 1 or 2. The first level belongs to the directed percolation or the parity-conserving (PC) universality class, the second to PC. If both levels are critical, the active region of the second level becomes heterogeneous. In the so-called coupled region the first level feeds particles to the second, while in the uncoupled region the second level evolves autonomously. Measuring dynamic critical exponents in both regions, we show to what extent the critical behavior of the second level depends on the universality class of the first. These results suggest a simple criterion for the emergence of unusual critical behavior of unidirectionally coupled nonequilibrium systems.