Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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3 citations
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01 Dec 2016TL;DR: A sufficient condition which ensures the asymptotic stability in probability of this class of systems is given using a Lyapunov approach.
Abstract: In this paper, we deal with asymptotic stability in probability of a class of stochastic systems, which is described by a stochastic differential equation having a square root on the diffusion part. This type of equations are usually used for the modeling of some systems such as population dynamics. A sufficient condition which ensures the asymptotic stability in probability of this class of systems is given using a Lyapunov approach.
3 citations
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TL;DR: In this paper, the authors applied the asymptotic method of Belinskii, Khalatnikov and Lifshitz to the study of the behavior near singularities of generic Bianchi IX cosmological models in the framework of the R2 theory of gravity.
Abstract: The asymptotic method of Belinskii, Khalatnikov and Lifshitz is applied to the study of the behavior near singularities of generic Bianchi IX cosmological models in the framework of the R2 theory of gravity Three main kinds of asymptotic forms for the metric are obtained: a de Sitter geometry, a monotonic fall on a curvature singularity after a finite number of oscillations, an infinite sequence of regular oscillations No chaos appears
3 citations
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3 citations
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TL;DR: The direct scheme, consisting of an immediate substitution of a postulated asymptotic expansion of a solution into the problem condition and finding a family of control problems to define the terms of the asymPTotic expansion, results in the asylptotic solution of the considered problem.
3 citations