(G, mu)-quadratic stochastic operators

作者：Blath J; Jamilov U U^*; Scheutzow M

来源：Journal of Difference Equations and Applications, 2014, 20(8): 1258-1267.

DOI：10.1080/10236198.2014.906591

• quadratic stochastic operator
• Volterra and non-Volterra operators
• evolutionary operator

We consider a new subclass of quadratic stochastic (evolutionary) operators on the simplex indexed by a finite Abelian group G with heredity law mu. With the help of the notion of s(mu)-invariant subgroups, where s(mu) denotes the support of mu in G, we prove that the trajectories of such operators always converge either to a periodic orbit or to a fixed point (where the latter holds for Lebesgue-almost all initial values). In particular, these operators are ergodic and almost regular. We also consider the speed of convergence to the limit, respectively, to the periodic orbit and give criteria to distinguish between regularity and periodicity.

• 出版日期2014