可积与混沌的四维Lotka-Volterra模型及种群可持续性
Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability
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中文总结 AI 辅助
本文研究四维Lotka-Volterra模型，发现其解可积时导致非可持续动力学，混沌时物种共存，并通过Lyapunov指数和Poincare截面揭示可持续性结构。
中文摘要 AI 辅助
我们研究了一个描述四种物种间相互作用的捕食者-猎物模型的四维推广。我们证明这些系统展现出丰富的渐近行为，其解要么是可积的，导致以种群无界增长或崩溃为特征的非可持续动力学，要么是混沌的，其中所有物种随时间共存。此外，我们回顾了可积情形，这些情形被分类为双参数族，并考察了与已知双参数可积情形行为相似的三参数族。我们还分析了混沌Lotka-Volterra模型的Lyapunov指数和Poincare截面，这些分析揭示了与可持续动力学预期相符的潜在结构。
英文摘要
We examine a 4-dimensional generalization of predator-prey models describing interactions among four species. We show that these systems exhibit a rich variety of asymptotic behaviors, with solutions that are either integrable, leading to non-sustainable dynamics characterized by unbounded population growth or collapse, or chaotic, where all species coexist over time. Moreover, we review the integrable cases, which are classified into two-parametric families, and examine three-parametric families that behave similarly to the known two-parametric integrable cases. We also analyze chaotic Lotka-Volterra models in terms of their Lyapunov exponents and Poincare' surfaces of section, which turn out to reveal underlying structures that are compatible with what is expected from sustainable dynamics.
发表机构
- College of Health and Science, University of Lincoln（林肯大学健康与科学学院）
- School of Computing and Digital Media, London Metropolitan University（伦敦城市大学计算与数字媒体学院）
- Department of Electrical and Computer Engineering, University of Peloponnese（伯罗奔尼撒大学电气与计算机工程系）
- Department of Mathematics, University of Patras（帕特雷大学数学系）
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