Attractors in coherent systems of differential equations

TL;DR

This paper characterizes attractors in a broader class of coherent dynamical systems, extending known results from cooperative systems and providing new insights into their attractor structures.

Contribution

It introduces new characterizations of attractors in coherent systems, generalizing results from cooperative systems and exploring the role of feedback loops.

Findings

Nontrivial periodic orbits cannot be attractors in coherent systems

New characterizations of attractors for coherent systems

Several results extend cooperative system theory

Abstract

Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor. This paper provides characterizations of attractors for the wider class of coherent systems, defined by the property that no directed feedback loops are negative. Several new results for cooperative systems are obtained in the process.