On Metzler positive systems on hypergraphs

• DOI: 10.48550/arxiv.2401.03652
• Publication Date: 2024-01-01
• Authors: Shaoxuan Cui; Guofeng Zhang; Hildeberto Jardón...; Ming Cao
• Keywords: Hypergraph; Adjacency matrix; Algebraic connectivity; Adjacency list; Algebraic graph theory

In graph-theoretical terms, an edge in a graph connects two vertices while hyperedge of hypergraph any more than one vertices. If the hypergraph's hyperedges further connect same number vertices, it is said to be uniform. algebraic theory, can characterized by adjacency matrix, and similarly, uniform tensor. This similarity enables us extend existing tools matrix analysis for studying dynamical systems evolving on graphs study class polynomial hypergraphs utilizing properties tensors. To precise, this paper, we first concept Metzler tensor then describe some useful such Next, focus positive associated with More importantly, design control laws stabilize origin hypergraphs. end, apply our findings classic systems: higher-order Lotka-Volterra population dynamics system SIS epidemic dynamic process. The corresponding novel stability results are accompanied ample numerical examples.