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math.DS2026
Almost-global convergence to twisted states in discrete Huygens rings
Jorge Buescu, Henrique M. Oliveira
We study the discrete Huygens phase map on the ring , the simplest oscillator network in which the coupling can be frustrated. Reciprocal coupling favours phase opposition bet…
math.DS2026
**Winding number forces universal synchronisation**
Jorge Buescu, Henrique M. Oliveira
We prove that two completely different oscillators synchronise through arbitrarily weak reciprocal impulses. Any two planar oscillators with hyperbolic attracting limit cycles and…
math.DS2026
Morse-Smale dynamics in discrete Huygens networks
Jorge Buescu, Emma D'Aniello, Henrique M. Oliveira
We study discrete networks of identical phase oscillators with positive reciprocal weights and smooth odd periodic interactions, motivated by discrete models of Huygens synch…