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A class of nonergodic Lotka-Volterra operators

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Abstract

On the basis of some numerical calculations, Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich’s example to the class of quadratic stochastic Volterra operators acting on a 2D simplex. In this paper, we provide a class of nonergodic Lotka-Volterra operators which includes all previous operators used in this context.

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References

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Authors and Affiliations

  1. International Islamic University of Malaysia, Kuantan, Malaysia

    M. Saburov

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  1. M. Saburov
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Correspondence to M. Saburov.

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The article was submitted by the author for the English version of the journal.

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Saburov, M. A class of nonergodic Lotka-Volterra operators. Math Notes 97, 759–763 (2015). https://doi.org/10.1134/S0001434615050107

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  • DOI: https://doi.org/10.1134/S0001434615050107

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