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The two-dimensional contact process (CP) with a competitive dynamics proposedby Martins {\it et al.} [Phys. Rev. E {\bf 84}, 011125(2011)] leads to theappearance of an unusual active asymmetric phase, in which the systemsublattices are unequally populated. It differs from the usual CP only by thefact that particles also interact with their next-nearest neighbor sites via adistinct strength creation rate and for the inclusion of an inhibition effect,proportional to the local density. Aimed at investigating the robustness ofsuch asymmetric phase, in this paper we study the influence of distinctinteractions for two bidimensional CPs. In the first model, the interactionbetween first neighbors requires a minimal neighborhood of adjacent particlesfor creating new offspring, whereas second neighbors interact as usual (e.g. atleast one neighboring particle is required). The second model takes theopposite situation, in which the restrictive dynamics is in the interactionbetween next-nearest neighbors sites. Both models are investigated under meanfield theory (MFT) and Monte Carlo simulations. In similarity with results byMartins {\it et. al.}, the inclusion of distinct sublattice interactionsmaintain the occurrence of an asymmetric active phase and reentrant transitionlines. In contrast, remarkable differences are presented, such as discontinuousphase transitions (even between the active phases), the appearance oftricritical points and the stabilization of active phases under larger valuesof control parameters. Finally, we have shown that the critical behaviors arenot altered due to the change of interactions, in which the absorbingtransitions belong to the directed percolation (DP) universality class, whereassecond-order active phase transitions belong to the Ising universality class.

Contact processes with competitive dynamics in bipartite lattices: Effects of distinct interactions