3 papers
math.DS2025
Morse Index Classification and Landscape of Kuramoto System for Hebbian-based Binary Pattern Recognition
Xiaoxue Zhao, Xiang Zhou
This study examines the Kuramoto model with a Hebbian learning rule and second-order Fourier coupling for binary pattern recognition. The system stores memorized binary patterns as…
math.DS2025
Enhanced Error-free Retrieval in Kuramoto-type Associative-memory Networks via Two-memory Configuration
Zhuchun Li, Xiaoxue Zhao, Xiang Zhou
We study the associative-memory network of Kuramoto-type oscillators that stores a set of memorized patterns (memories). In [Phys. Rev. Lett., 92 (2004), 108101], Nishikawa, Lai an…
math.DS2024
Critical Points, Stability, and Basins of Attraction of Three Kuramoto Oscillators with Isosceles Triangle Network
Xiaoxue Zhao, Xiang Zhou
This article investigates the Kuramoto model with three oscillators that are interconnected by an isosceles triangle network. The characteristic of this model is that the coupling…