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Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

Rawad Abdulghafor;  Farruh Shahidi;  Akram Zeki;  Sherzod Turaev — 2016

Open Mathematics

The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications...

Concurrently controlled grammars

Gairatzhan Mavlankulov;  Mohamed Othman;  Sherzod Turaev;  Mohd Hasan Selamat;  Laula Zhumabayeva;  Tamara Zhukabayeva — 2018

Kybernetika

This paper introduces a new variant of Petri net controlled grammars, namely a concurrently controlled grammar, where the control over the application of the productions of a grammar is realized by a Petri net with different parallel firing strategies. The generative capacity of these grammars is investigated with respect to transition labeling strategies, definitions of final marking sets and parallel transition firing modes. It is shown that the labeling strategies do not effect the computational...

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