Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916529508974592 |
|---|---|
| author | La Luz, Diego Rojas Craciun, Gheorghe Yu, Polly Y. |
| author_facet | La Luz, Diego Rojas Craciun, Gheorghe Yu, Polly Y. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems La Luz, Diego Rojas Craciun, Gheorghe Yu, Polly Y. Dynamical Systems Molecular Networks Populations and Evolution 37C10, 37N25, 92D25, 34D23, 92C42, 80A30 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. |
| title | Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems |
| topic | Dynamical Systems Molecular Networks Populations and Evolution 37C10, 37N25, 92D25, 34D23, 92C42, 80A30 |
| url | https://arxiv.org/abs/2412.13367 |