A theoretical and computational study of heteroclinic cycles in Lotka-Volterra systems.

M C Bortolan, P Kalita, J A Langa, R O Moura

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Article in Journal of mathematical biology, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

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A general framework for invasion cycles in ecology.Ecology · 2026
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4 authors.

M C BortolanDepartamento de Matemática, Centro de Ciências Físicas e Matemt́icas, Universidade Federal de Santa Catarina, Campus Florianópolis, Florianópolis, SC, CEP 88040-090, Brazil.

P KalitaFaculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland.

J A LangaDepartamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Campus Reina Mercedes, 41012, Sevilla, Spain. langa@us.es.ORCID 0000-0002-8765-0764

R O MouraInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, São Carlos, SP, Caixa Postal 668, Brazil.

Funding

CAPES 88887.828519/2023-00FAPESP 2023/11798-5Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España PID2021-122991NB-C21NCN UMO2016/22/A/ST1/00077

6 · The paper itself

Abstract

In general, global attractors are composed of isolated invariant sets and the connections between them. This structure can possibly be highly complex, encompassing attraction basins, repeller sets and invariant sets that, collectively, form a dynamical landscape. Lotka-Volterra systems have long been pivotal as preliminary models for dynamics in complex networks exhibiting pairwise interactions. In scenarios involving Volterra-Lyapunov (VL) stable matrices, the dynamics is simplified in such a way that the positive solutions converge to a single, globally asymptotically stable stationary point as time tends to infinity, thereby excluding the existence of periodic solutions. In this work, we conduct a systematic study on the emergence of heteroclinic cycles within Lotka-Volterra systems characterized by Volterra-Lyapunov stable matrices. Although VL stability of the matrix implies that

Indexed as

Models, BiologicalComputational BiologyComputer SimulationHumansMathematical ConceptsAlpha-limitsCycle structureInvasion graphLotka–VolterraVolterra–Lyapunov matrix

Identifiers

PMID39920400

DOI10.1007/s00285-025-02190-4

PMCPMC11805806

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