关于逻辑型微分方程的说明

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Reports on Mathematical Physics Pub Date : 2024-06-01 DOI:10.1016/S0034-4877(24)00039-9
G. Dattoli, R. Garra
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引用次数: 0

摘要

逻辑方程在研究任何表现出增长和饱和的非线性演变过程中都起着举足轻重的作用。人们对它们所统治的现象学的兴趣远远超出了物理过程,涵盖了生态学、人口增长、经济等许多方面。. .根据如此广泛的应用范围,有不同形式的函数和分布被认为是广义物流。有时,它们是通过拟合程序得到的。因此,可能需要一些标准来推断相关的非线性微分方程,以便猜测 "隐藏的 "演变机制。在本文中,我们分析了不同形式的物流函数,并使用简单的方法重建它们所满足的微分方程。我们的研究还包括包含非标准形式导数算子的微分方程,如拉盖尔类型的微分方程。
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A note on differential equations of logistic type

Logistic equations play a pivotal role in the study of any nonlinear evolution process exhibiting growth and saturation. The interest for the phenomenology they rule goes well beyond physical processes and covers many aspects of ecology, population growth, economy. . . According to such a broad range of applications, there are different forms of functions and distributions which are recognized as generalized logistics. Sometimes they are obtained by fitting procedures. Therefore, criteria might be needed to infer the associated nonlinear differential equations, useful to guess “hidden” evolution mechanisms. In this article we analyze different forms of logistic functions and use simple means to reconstruct the differential equation they satisfy. Our study includes also differential equations containing nonstandard forms of derivative operators, like those of the Laguerre type.

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来源期刊
Reports on Mathematical Physics
Reports on Mathematical Physics 物理-物理:数学物理
CiteScore
1.80
自引率
0.00%
发文量
40
审稿时长
6 months
期刊介绍: Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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