| 1. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
- 2018
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In: Bulletin of the Malaysian Mathematical Sciences Society. - : Springer Science and Business Media LLC. - 0126-6705 .- 2180-4206. ; 41:1, s. 159-173
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Journal article (peer-reviewed)abstract
- This paper is devoted to the study of the problem of prevalence in the classof quadratic stochastic operators acting on the L1 space for the uniform topology.We obtain that the set of norm quasi-mixing quadratic stochastic operators is a denseand open set in the topology induced by a very natural metric. This shows the typicallong-term behaviour of iterates of quadratic stochastic operators.
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| 2. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
- 2013
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In: Proceedings of the XIX National Conference on Applications of Mathematics in Biology and Medicine. - 8360253862 ; , s. 19-24
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Conference paper (peer-reviewed)abstract
- Quadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introducedand studied recently. In the present work we discuss biological interpretations that can be attributedto them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.
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| 3. |
- Bartoszek, Krzysztof, 1984-, et al.
(author)
-
Weak Stability of Centred Quadratic Stochastic Operators
- 2019
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In: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY. - : MALAYSIAN MATHEMATICAL SCIENCES SOC. - 0126-6705 .- 2180-4206. ; 42:4, s. 1813-1830
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Journal article (peer-reviewed)abstract
- We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits. It is shown that for the existence of a weak limit, it is sufficient that the distributions of the trait and the perturbation have a finite variance or have tails controlled by a suitable power function. In particular, probability distributions from the domain of attraction of stable distributions have found an application, although in general the limit is not stable.
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