Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks

2025/01/02 by Xue, Shuyue, Maghrebi, Mohammad, Mias, George I. +1 · 1 citation
#Biological Physics (physics.bio-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Biological sciences #FOS: Physical sciences #Molecular Networks (q-bio.MN) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2501.00983

Abstract

We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycle attractors. The limit cycle phase is bounded by two critical regions: a Hopf bifurcation line and a fold bifurcation line, each with unique dynamical critical exponents and sensitivity to perturbations. A Master Equation approach numerically verifies the critical behavior predicted analytically. We discuss how these networks could model biological processes near a critical threshold of cyclic instability evolving through multi-step transitions.

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