Rank of Stably Dissipative Graphs

TL;DR

This paper demonstrates that for stably dissipative Lotka-Volterra systems, the rank of the defining matrix, which indicates the system's invariant foliation dimension, can be fully determined by the system's graph structure.

Contribution

It establishes a direct link between the graph structure of stably dissipative systems and the rank of their defining matrices, providing a graph-based characterization.

Findings

The rank is completely determined by the graph.

Graph structure encodes the invariant foliation dimension.

Provides a method to compute rank from graph properties.

Abstract

For the class of stably dissipative Lotka-Volterra systems we prove that the rank of its defining matrix, which is the dimension of the associated invariant foliation, is completely determined by the system's graph.