A Quasi-strictly Non-volterra Quadratic Stochastic Operator
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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.
KeywordsQuadratic stochastic operator Simplex Trajectory Volterra and non-Volterra operators
Mathematics Subject ClassificationPrimary 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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