二阶泊松代数和可积Lotka - Volterra系统的Lambert \(W\)函数解

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2024-12-20 DOI:10.1134/S1560354724580032

Peter H. van der Kamp, David I. McLaren, G. R. W. Quispel

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引用次数: 0

摘要

研究了一类可积非齐次Lotka - Volterra系统，该系统的二次项由一个反对称矩阵定义，其线性项由三个块组成。我们给出了它们的达布多项式的泊松代数，并证明了一个收缩定理。然后，我们使用这些结果根据功能独立（对于某些，交换）积分的数量对系统进行分类。我们还通过正交建立了可分性/可解性，给出了二维和三维系统的解，我们用Lambert \(W\)函数提供了这些解。

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On a Quadratic Poisson Algebra and Integrable Lotka – Volterra Systems with Solutions in Terms of Lambert’s \(W\) Function

We study a class of integrable inhomogeneous Lotka – Volterra systems whose quadratic terms are defined by an antisymmetric matrix and whose linear terms consist of three blocks. We provide the Poisson algebra of their Darboux polynomials and prove a contraction theorem. We then use these results to classify the systems according to the number of functionally independent (and, for some, commuting) integrals. We also establish separability/solvability by quadratures, given the solutions to the 2- and 3-dimensional systems, which we provide in terms of the Lambert \(W\) function.

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.