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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TL;DR: In this paper, transient and asymptotic behaviors of general Markov fluid models are studied and analyzed, and methods to apply to a general MarkOV fluid model and the numerical results are interpreted.
Abstract: In this paper, transient and asymptotic behaviors of general Markov fluid models are studied and analyzed. The input and output rates are assumed to be modulated by a finite state irreducible Markov process, which can admit states with zero effective input rate. The main advantage of the proposed methods is their accuracy and their numerical stability. For the transient solution, properties of stationary detection lead to reduce considerably the computational complexity of the algorithm. As for the asymptotic solution, it is derived from the transient one's. We apply these methods to a general Markov fluid model and we interpret the numerical results.
8 citations
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TL;DR: In this paper, the conditions of asymptotic stability of second-order linear dynamic equations on time scales were examined, and the stability estimates were established by using integral representations of the solutions via asymPTotic solutions, error estimates, and calculus.
Abstract: We examine the conditions of asymptotic stability of second-order linear dynamic equations on time scales. To establish asymptotic stability we prove the stability estimates by using integral representations of the solutions via asymptotic solutions, error estimates, and calculus on time scales.
8 citations
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TL;DR: In this article, the asymptotic behavior of all solutions to the fourth-order Emden-Fowler type differential equation with singular nonlinearity is investigated, where the equation is transformed into a system on the three-dimensional sphere.
Abstract: The asymptotic behavior of all solutions to the fourth-order Emden– Fowler type differential equation with singular nonlinearity is investigated. The equation is transformed into a system on the three-dimensional sphere. By investigation of the asymptotic behavior of all possible trajectories of this system an asymptotic classification of all solutions to the equation is obtained.
8 citations
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8 citations
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09 May 2016
TL;DR: In this article, an asymptotic perturbation of the limit set generated from a nitely family of conformal contraction maps endowed with a directed graph was studied, and it was shown that the Hausdor dimension of the restricted limit set behaves in the same order.
Abstract: We study an asymptotic perturbation of the limit set generated from a nitely family of conformal contraction maps endowed with a directed graph. We show that if those maps have asymptotic expansions under weak conditions, then the Hausdor dimension of the limit set behaves asymptotically by the same order. We also prove that the Gibbs measure of a suitable potential and the measure theoretic entropy of this measure have asymptotic expansions under an additional condition. In nal section, we demonstrate degeneration of graph iterated function systems. Mathematics Subject Classi cation (2010). Primary: 37B10; Secondary: 37C45, 37D35.
8 citations