We study a competitive two-species ($A$ and $B$) reaction-diffusion model on a bipartite square lattice, where cooperative interactions lead to either particle coalescence or dispersal. The model is controlled by a coalescence-dispersion parameter $g$ and a maximum site occupancy per species, $n_o$. We investigate the system's phase transitions from an active to an absorbing state using both a site-based mean field approximation and Monte Carlo (MC) simulations. For single occupancy $(n_o=1)$, we find a discontinuous, first-order phase transition at a transition point $g_c=1$. The mean field calculations reveal a manifold of solutions at this point, leading to bistability between an active phase and an ordered, chessboardlike absorbing state—a mechanism of dynamic bistability confirmed by simulations. For multi-occupancy cases $(n_o\ge 2)$, the transition remains first order but occurs for $g_c<1$. Here, the absorbing phase is an infinitely degenerate manifold of disordered, jammed configurations. MC simulations show that the transition point $g_c$ increases with $n_o$ for $n_o\ge 2$. This trend seems to be driven by the role of coalescence as an antisegregation mechanism. As $n_o$ increases, the system becomes denser, enhancing this mixing effect and thus requiring a stronger dispersal probability (a higher $g_c$) to induce the transition to the segregated absorbing state. In this model, the site's storage capacity strongly alters the macroscopic transition mechanism.

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• First order phase transitions
• Irreversible processes