Достаточное условие кубического оператора для сохранения симплекса

There is a one-to-one correspondence between cubic operators that map Rm to itself and m4-dimensional matrices. It is known that any cubic operator associated with a stochastic (in a fixed sense) m4-dimensional matrix preserves the standard simplex. In this paper, we establish a sufficient conditions on the non-stochastic m4-dimensional matrix that ensure the corresponding cubic operator also preserves the simplex. Furthermore, on the two-dimensional simplex we investigate the dynamics of a cubic operator defined by a non-stochastic matrix