Discontinuous transition to chaos in a canonical random neural network
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916310173089792 |
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| author | Pazó, Diego |
| author_facet | Pazó, Diego |
| contents | We study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. We generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice $ϕ(x)=\tanh x$. A discontinuous transition to chaos occurs whenever the slope of $ϕ$ at 0 is a local minimum (i.e., for $ϕ'''(0)>0$). Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discontinuous transition to chaos in a canonical random neural network Pazó, Diego Chaotic Dynamics Neurons and Cognition We study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. We generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice $ϕ(x)=\tanh x$. A discontinuous transition to chaos occurs whenever the slope of $ϕ$ at 0 is a local minimum (i.e., for $ϕ'''(0)>0$). Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos. |
| title | Discontinuous transition to chaos in a canonical random neural network |
| topic | Chaotic Dynamics Neurons and Cognition |
| url | https://arxiv.org/abs/2405.14607 |