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


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.


Quadratic stochastic operator Simplex Trajectory Volterra and non-Volterra operators 

Mathematics Subject Classification

Primary 37N25 Secondary 92D10 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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