Behavior of Trajectories of a Quadratic Operator

Abstract

We consider a two-parametric quadratic stochastic operator (QSO) mapping 3-dimensional simplex to itself. To date, for very few QSOs complete description of trajectories (limit points) is known. For our two-parametric QSO we completely describe the set of all limit points of trajectories. Namely, we find unique fixed point and the set of all (a continuum set) 2-periodic points and show that each such a point is non-hyperbolic. Moreover, for any initial point (taken from the 3-dimensional simplex) we find an invariant set containing the initial point and a unique 2-periodic orbit of the operator, such that the trajectory of initial point converges to this 2-periodic orbit.

Topics

Identifiers

DOI

10.1134/s1995080223070387

Citations and references