Discontinuous transition to chaos in a canonical random neural network.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 39161016.
- Also identified by DOI 10.1103/PhysRevE.110.014201.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
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)=tanhx. 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.