Qualitative stability of nonlinear networked systems

TL;DR

This paper extends classical linear sign stability criteria to nonlinear networked systems, providing simple sufficient conditions for stability based solely on the sign patterns of interactions, applicable to complex biological and economic systems.

Contribution

It introduces a novel extension of sign stability criteria from linear to nonlinear systems, enabling stability assessment with minimal information.

Findings

Provides simple sufficient conditions for nonlinear system stability

Applicable to large biological and economic networks

Enhances understanding of qualitative stability in complex systems

Abstract

In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.