恒温器中并存的中性稳定周期轨道的多重性(受周期性移除率的影响

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Thomas Guilmeau, Alain Rapaport
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引用次数: 0

摘要

SIAM 应用数学杂志》第 84 卷第 1 期第 39-59 页,2024 年 2 月。 摘要我们确定了多物种恒温模型中生长函数的分类学性质,该性质确保了在周期性去除率下物种子集的共存。我们证明,物种密度的某些幂的比例是周期函数,导致无穷多个不同的中性稳定周期轨道,这取决于初始条件。这种中性稳定的物种条件具有与给定平均值的周期信号形状无关的特点。我们还给出了允许两个不同物种子集共存的条件。虽然这些条件是非通用的,但我们通过模拟证明,当这些条件仅近似满足时,在很长的时间间隔内,解的行为接近于非通用情况,这证明了我们的研究是有意义的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multiplicity of Neutrally Stable Periodic Orbits with Coexistence in the Chemostat Subject to Periodic Removal Rate
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 39-59, February 2024.
Abstract. We identify a taxonomic property on the growth functions in the multispecies chemostat model which ensures the coexistence of a subset of species under periodic removal rate. We show that proportions of some powers of the species densities are periodic functions, leading to an infinity of distinct neutrally stable periodic orbits depending on the initial condition. This condition on the species for neutral stability possesses the feature to be independent of the shape of the periodic signal for a given mean value. We also give conditions allowing the coexistence of two distinct subsets of species. Although these conditions are nongeneric, we show in simulations that when these conditions are only approximately satisfied, the behavior of the solutions is close to that of the nongeneric case over a long time interval, justifying the interest of our study.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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