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Qualitative Theory of Dynamical Systems

, Volume 18, Issue 3, pp 1013–1029 | Cite as

A Quasi-strictly Non-volterra Quadratic Stochastic Operator

  • A. J. M. Hardin
  • U. A. RozikovEmail author
Article
  • 25 Downloads

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.

Keywords

Quadratic stochastic operator Simplex Trajectory Volterra and non-Volterra operators 

Mathematics Subject Classification

Primary 37N25 Secondary 92D10 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of OklahomaNormanUSA
  2. 2.Institute of MathematicsTashkentUzbekistan

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