Qualitative stability of nonlinear networked systems
It addresses the problem of stability analysis in large nonlinear systems (e.g., biology, economics) where only sign information is available, offering a qualitative tool for practitioners.
The paper extends classical linear sign stability criteria to nonlinear networked systems, providing simple sufficient conditions to determine stability using only the sign patterns of interactions, which is crucial for systems where dynamics are coarsely known.
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.