Year: 2026
Type: preprint
Abstract: We study discrete networks of $N+1$ identical phase oscillators with positive reciprocal weights and smooth odd periodic interactions, motivated by discrete models of Huygens synchronisation. The interaction laws define an intrinsic potential, and removing the common phase gives a gradient map on the $N$-torus. A weighted graph Laplacian yields explicit step sizes for strict Lyapunov decrease and global invertibility. Our main result is a Morse--Smale criterion for maps $z\mapsto z+hK\sin z$: if $K$ is symmetric, nonsingular and weakly diagonally dominant, the map is Morse--Smale for $0
Source: arXiv (Cornell University)
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221068255