Equilibrium state as a compromise in the struggle of opponents

Mathematical models describing the conflict interaction between alternative opponents are studied. It is assumed that the adversaries are indestructible, located in different regions of the resource space, and receive external support in their struggle with each other. The main questions concern the compromise states of equilibrium (a certain type of fixed points) of the associated dynamic conflict system. Namely, the existence of such states, their stability, and the dominant side in each region. It has been established that states of equilibrium compromise arise only in the presence of external influences (supports) necessarily for both opponents and only some of them are stable with non-trivial basins of attraction. It was also found that with insufficient external support, the dominant opponent in each of the regions can sharply lose its position.