一类广义半马尔可夫种群动力学模型的长期行为

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-30 DOI:10.1002/mma.70008

Katarzyna Pichór, Ryszard Rudnicki

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引用次数: 0

摘要

给出了半马尔可夫过程的一些推广应用。一般模型用具有初始边界条件的一阶偏微分方程来描述。它涵盖了各种生物模型，包括那些由分段确定性马尔可夫过程描述的模型以及先进的随机混合系统。在与该模型相关的可积函数空间上构造了一个正算子半群。我们研究了所选模型的解的长期行为：表型模型和具有灾害的随机种群增长模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Long-Time Behavior of a Generalized Semi-Markov Model of Population Dynamics

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Long-Time Behavior of a Generalized Semi-Markov Model of Population Dynamics

We present applications of some generalization of semi-Markov processes. The general model is described by a first-order partial differential equation with initial-boundary conditions. It covers a variety of biological models including those described by piecewise deterministic Markov processes as well as advanced stochastic hybrid systems. We construct a semigroup of positive operators on the space of integrable functions related to this model. We study long-time behavior of solutions of selected models: phenotypic models and a stochastic population growth model with disasters.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.