Stability and monotonicity of Lotka–Volterra type operators

In the present paper,we investigate stability of trajectories ofLotka–Volterra (LV) type operators defined in finite dimensional simplex.We prove that any LV type operator is a surjection of the simplex. It is introduced a newclass of LV-type operators, called MLV type ones, and we show that trajectories of the introduced operators converge. Moreover, we show that such kind of operators have totally different behavior than f-monotone LV type operators