The Stability Matrix Spectrum of Large Ecological and Economical Systems

Author:

Nirbhay Patil, Fabian Aguirre-Lopez, Jean-Philippe Bouchaud

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

date:

2023-12-18 00:00:00

Abstract

Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations. We find analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.

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