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A Quasi-strictly Non-volterra Quadratic Stochastic Operator

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Abstract

We consider a four-parameter family of non-Volterra operators defined on the two-dimensional simplex and show that, with one exception, each such operator has a unique fixed point. Depending on the parameters, we establish the type of this fixed point. We study the set of \(\omega \)-limiting points for each trajectory and show that this set can be a single point or can contain a 2-periodic trajectory.

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Acknowledgements

The first author was supported by the National Science Foundation, Grant No. 1658672. We thank the referees for their helpful comments.

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Authors and Affiliations

  1. University of Oklahoma, 660 Parrington Oval, Norman, OK, 73019, USA

    A. J. M. Hardin

  2. Institute of Mathematics, 81, Mirzo Ulug’bek str., Tashkent, Uzbekistan, 100125

    U. A. Rozikov

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  1. A. J. M. Hardin
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  2. U. A. Rozikov
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Correspondence to U. A. Rozikov.

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Hardin, A.J.M., Rozikov, U.A. A Quasi-strictly Non-volterra Quadratic Stochastic Operator. Qual. Theory Dyn. Syst. 18, 1013–1029 (2019). https://doi.org/10.1007/s12346-019-00325-9

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  • DOI: https://doi.org/10.1007/s12346-019-00325-9

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