On convergence of trajectories of a non-volterra quadratic stochastic operator

In the present paper we consider a non-Volterra quadratic stochastic operator defined on the two-dimensional simplex. We showed that the center of the simplex is a unique fixed p oint o f t his o perator a nd i t h as a ttracting t ype. We c onstructed a Lyapunov function and using it we showed that for any initial point the trajectory of this operator approaches to the center of the simplex.

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