# Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems

Source: [Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems](<https://www.sota2.com/research/paper/68fa5cbf1e209131ce9d3de7>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:50:20.468Z

Authors: Diego Rojas La Luz, Gheorghe Craciun, Polly Y. Yu

Published: 2024-12-17T22:47:19.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2412.13367>)

[PDF](<https://arxiv.org/pdf/2412.13367.pdf>)