Chaos in high-dimensional dynamical systems with tunable non-reciprocity
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908965570347008 |
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| author | Fournier, Samantha Urbani, Pierfrancesco |
| author_facet | Fournier, Samantha Urbani, Pierfrancesco |
| contents | High-dimensional dynamical systems of interacting degrees of freedom are ubiquitous in the study of complex systems. When the directed interactions are totally uncorrelated, sufficiently strong and non-linear, many of these systems exhibit a chaotic attractor characterized by a positive maximal Lyapunov exponent (MLE). On the contrary, when the interactions are completely symmetric, the dynamics takes the form of a gradient descent on a carefully defined cost function, and it exhibits slow dynamics and aging. In this work, we consider the intermediate case in which the interactions are partially symmetric, with a parameter α tuning the degree of non-reciprocity. We show that for any value of α for which the corresponding system has non-reciprocal interactions, the dynamics lands on a chaotic attractor. Correspondingly, the MLE is a non-monotonous function of the degree of non-reciprocity. This implies that conservative forcing deriving from the gradient field of a rough energy landscape can make the system more chaotic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04702 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chaos in high-dimensional dynamical systems with tunable non-reciprocity Fournier, Samantha Urbani, Pierfrancesco Disordered Systems and Neural Networks High-dimensional dynamical systems of interacting degrees of freedom are ubiquitous in the study of complex systems. When the directed interactions are totally uncorrelated, sufficiently strong and non-linear, many of these systems exhibit a chaotic attractor characterized by a positive maximal Lyapunov exponent (MLE). On the contrary, when the interactions are completely symmetric, the dynamics takes the form of a gradient descent on a carefully defined cost function, and it exhibits slow dynamics and aging. In this work, we consider the intermediate case in which the interactions are partially symmetric, with a parameter α tuning the degree of non-reciprocity. We show that for any value of α for which the corresponding system has non-reciprocal interactions, the dynamics lands on a chaotic attractor. Correspondingly, the MLE is a non-monotonous function of the degree of non-reciprocity. This implies that conservative forcing deriving from the gradient field of a rough energy landscape can make the system more chaotic. |
| title | Chaos in high-dimensional dynamical systems with tunable non-reciprocity |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2601.04702 |