Non-hyperbolic trajectory of a quasi-non-Volterra cubic stochastic operator
Non-hyperbolic trajectory of a quasi-non-Volterra cubic stochastic operator
DOI:
https://doi.org/10.56143/ujmcs.v1i2.2Keywords:
кубический стохастический оператор, квазиневольтерровский кубический стохастический оператор, функция Ляпунова, траектория, предельное множество.Abstract
In this paper, we consider the dynamics of a quasi-non-Volterra cubic stochastic operator defined on the 2D simplex.
We find the invariant set of this operator and show that it has a unique non-hyperbolic fixed point. Furthermore,
we construct and use the Lyapunov function to prove that the set of limit points of a trajectory for any initial point
is unique.
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