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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.19127 |
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| _version_ | 1866910023708311552 |
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| author | Poggialini, Anna Di Santo, Serena Villegas, Pablo Gabrielli, Andrea Muñoz, Miguel A. |
| author_facet | Poggialini, Anna Di Santo, Serena Villegas, Pablo Gabrielli, Andrea Muñoz, Miguel A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-normal Dynamics on Non-reciprocal Networks: Reactivity and Effective Dimensionality in Neural Circuits Poggialini, Anna Di Santo, Serena Villegas, Pablo Gabrielli, Andrea Muñoz, Miguel A. Biological Physics 37N20 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. |
| title | Non-normal Dynamics on Non-reciprocal Networks: Reactivity and Effective Dimensionality in Neural Circuits |
| topic | Biological Physics 37N20 |
| url | https://arxiv.org/abs/2507.19127 |