A class of nonergodic lotka–volterra operators
On the basis of some numerical calculations,Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich...
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| Format: | Article |
| Language: | English |
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Pleiades Publishing
2015
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| Online Access: | http://irep.iium.edu.my/45054/ http://irep.iium.edu.my/45054/ http://irep.iium.edu.my/45054/1/Non_Ergodic_LV_Operator_---_MN.pdf |
| Summary: | On the basis of some numerical calculations,Ulam has conjectured that the ergodic theorem holds for any quadratic stochastic operator acting on a finite-dimensional simplex. However, Zakharevich showed that Ulam’s conjecture is false in general. Later, Ganikhodzhaev and Zanin generalized Zakharevich’s example to the class of quadratic stochastic Volterra operators acting on a 2D simplex. In this paper, we provide a class of nonergodic Lotka–Volterra operators which includes all previous operators used in this context. |
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