Distribution of quadruples according to their convergence times in the four-number game (Q1769344)

A specific nonlinear time discrete diffusion network called the four-number game is studied. It is shown that the dynamical behavior of a solution depends solely on the initial distribution; furthermore, every solution either converges to the trivial distribution or never converges. If a solution converges, the steps it takes to converge are determined; and if the contrary is true, the corresponding initial distributions are found.