Non-normal Dynamics on Non-reciprocal Networks: Reactivity and Effective Dimensionality in Neural Circuits

TL;DR

This paper explores how local and global non-reciprocal interactions in neural networks lead to complex, emergent dynamics such as fluctuation-driven transitions and dimensionality reduction, advancing understanding of non-normal systems.

Contribution

It introduces a unified framework analyzing the interplay of local and global non-normality in neural circuits using a modified Wilson-Cowan model.

Findings

Emergent collective dynamics from non-reciprocity

Fluctuation-driven transitions observed

Dimensionality reduction in network activity

Abstract

Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple levels: locally, in the dynamics of individual units, and globally, in the topology of their interactions. In this work, we investigate how these two forms of non-reciprocity interact in networks of neuronal populations. At the local level, each population is modeled by a non-reciprocally coupled set of excitatory and inhibitory neural populations exhibiting transient amplification and reactivity. At the network level, these populations are coupled via directed, asymmetric connections that introduce structural non-normality. Since non-reciprocal interactions generically lead to non-normal linear operators, we frame both local and global asymmetries in terms of non-normal dynamics. Using a modified Wilson-Cowan framework, we analyze how the interplay between these two types of non-normality shapes the system's behavior. We show that their combination leads to emergent collective dynamics, including fluctuation-driven transitions, dimensionality reduction, and novel nonequilibrium steady states. Our results provide a minimal yet flexible framework to understand how multi-scale non-reciprocities govern complex dynamics in neural and other interconnected systems.