First integrals of anti-symmetric replicator equations (Q2718011)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: First integrals of anti-symmetric replicator equations |
scientific article; zbMATH DE number 1606230
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | First integrals of anti-symmetric replicator equations |
scientific article; zbMATH DE number 1606230 |
Statements
21 January 2002
0 references
replicator equation
0 references
Lotka-Volterra equation
0 references
first integrals
0 references
graphs
0 references
First integrals of anti-symmetric replicator equations (English)
0 references
The authors study the system \(\dot x_i = x_i( \sum_{j=1}^n a_{ij}x_j)\), \(i=1,2,\ldots,n\), with an anti-symmetric real \(n\times n\)-matrix \(A\), i.e., \(A^T=-A\). The functions \(\varphi_1=x_1+\ldots+x_n\) and \(\varphi_n=\prod_{i=1}^n x_i^{p_i}\), with \((p_1,\ldots,p_n)\in \operatorname {Ker}A\), are first integrals. By using a combinatorial approach, additional first integrals are obtained.
0 references
