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arXiv · 2412.13367

Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems

Diego Rojas La Luz·Gheorghe Craciun·Polly Y. Yu
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Abstract

We study the global stability of generalized Lotka-Volterra systems with generalized polynomial right-hand side, without restrictions on the number of variables or the polynomial degree, including negative and non-integer degree. We introduce polyexponential dynamical systems, which are equivalent to the generalized Lotka-Volterra systems, and we use an analogy to the theory of mass-action kinetics to define and analyze complex balanced polyexponential systems, and implicitly analyze complex balanced generalized Lotka-Volterra systems. We prove that complex balanced generalized Lotka-Volterra systems have globally attracting states, up to standard conservation relations, which become linear for the associated polyexponential systems. In particular, complex balanced generalized Lotka-Volterra systems cannot give rise to periodic solutions, chaotic dynamics, or other complex dynamical behaviors. We describe a simple sufficient condition for complex balance in terms of an associated graph structure, and we use it to analyze specific examples.

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BibTeXRIS

Diego Rojas La Luz, Gheorghe Craciun, Polly Y. Yu. 2024-12-17. Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems. https://arxiv.org/abs/2412.13367

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