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arXiv · 1112.3423

The Limit Behavior Of The Trajectories of Dissipative Quadratic Stochastic Operators on Finite Dimensional Simplex

F. A. Shahidi·M. T. Abu Osman
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Abstract

The limit behavior of trajectories of dissipative quadratic stochastic operators on a finite-dimensional simplex is fully studied. It is shown that any dissipative quadratic stochastic operator has either unique or infinitely many fixed points. If dissipative quadratic stochastic operator has a unique point, it is proven that the operator is regular at this fixed point. If it has infinitely many fixed points, then it is shown that $ω-$ limit set of the trajectory is contained in the set of fixed points.

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F. A. Shahidi, M. T. Abu Osman. 2011-12-15. The Limit Behavior Of The Trajectories of Dissipative Quadratic Stochastic Operators on Finite Dimensional Simplex. https://doi.org/10.1142/s201019451200534x

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