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PreprintCC BY 4.0arXiv

Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability

  • H. Christodoulidi
  • T. E. Kouloukas
  • L. B. Drossos
  • T. Bountis
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{christodoulidi2026integrable,
  title = {{Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability}},
  author = {H. Christodoulidi and T. E. Kouloukas and L. B. Drossos and T. Bountis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13797},
  eprint = {2609.13797},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13797},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability
AU  - H. Christodoulidi
AU  - T. E. Kouloukas
AU  - L. B. Drossos
AU  - T. Bountis
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13797
UR  - https://arxiv.org/abs/2609.13797
AB  - 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.
ER  -