2025/03/26 by Samantha J. Fournier, Fournier, Samantha J., Alessandro Pacco +5 · 7 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2503.20908
openalex publication_date 2025/03/26 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/30
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the equations describing the system's dynamics exhibit a number of equilibria that is exponentially large in the dimensionality of the system, and these equilibria are all linearly unstable in the chaotic phase. Solving the effective equations governing the dynamics in the infinite-dimensional limit, we determine the typical properties (magnetization, overlap) of the configurations belonging to the attractor manifold. We show that these properties cannot be inferred from those of the equilibria, challenging the expectation that chaos can be understood purely in terms of the numerous unstable equilibria of the dynamical equations. We discuss the dependence of this scenario on the strength of non-reciprocity in the interactions. These results are obtained through a combination of analytical methods such as Dynamical Mean-Field Theory and the Kac-Rice formalism.