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arXiv · 1307.1265

(G,μ)- Quadratic Stochastic Operators

J. Blath·U. U. Jamilov·M. Scheutzow
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Abstract

We consider a new subclass of quadratic stochastic (evolutionary) operators on the simplex indexed by a finite Abelian group G with heredity law μ. With the help of the notion of s(μ)-invariant subgroups, where s(μ) denotes the support of μin G, we prove that almost all (w.r.t.\ Lebesgue measure) trajectories of such operators converge to a unique fixed point which is the center of the simplex. We also identify and describe the periodic trajectories of the operator and give conditions for regularity and periodicity.

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J. Blath, U. U. Jamilov, M. Scheutzow. 2013-07-04. (G,μ)- Quadratic Stochastic Operators. https://arxiv.org/abs/1307.1265

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