TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.4.100
TI  - Critical dynamics and cyclic memory retrieval in non-reciprocal Hopfield networks
PY  - 2025/10/16
UR  - https://www.scipost.org/SciPostPhys.19.4.100
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 4
SP  - 100
A1  - Xue, Shuyue
AU  - Maghrebi, Mohammad
AU  - Mias, George
AU  - Piermarocchi, Carlo
AB  - 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-cycles. The limit cycle phase is bounded by a Hopf bifurcation line and a fold bifurcation line. Autocorrelation scales as $\tilde{C}(\tau/N^\zeta)$, with $\zeta = 1/2$ on the Hopf line and $\zeta = 1/3$ on the fold line. Perturbations of strength $F$ on the Hopf line exhibit response times scaling as $|F|^{-2/3}$, while they induce switches in a controlled way within times scaling as $|F|^{-1/2}$ in the fold line. 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.
ER  -

@Article{10.21468/SciPostPhys.19.4.100,
	title={{Critical dynamics and cyclic memory retrieval in non-reciprocal Hopfield networks}},
	author={Shuyue Xue and Mohammad Maghrebi and George I. Mias and Carlo Piermarocchi},
	journal={SciPost Phys.},
	volume={19},
	pages={100},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.4.100},
	url={https://scipost.org/10.21468/SciPostPhys.19.4.100},
}