Anticipated synchronization in systems with distributed delay

David Ortiz del Campo; Tobias Galla; Raúl Toral

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arXiv · 2603.02918

Anticipated synchronization in systems with distributed delay

David Ortiz del Campo·Tobias Galla·Raúl Toral

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Abstract

Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a single delay time in the coupling term, for which exact anticipation can arise as a solution. Here we extend this framework to configurations with distributed delay times. Our main result is that, for a given delay distribution, approximate anticipated synchronisation can emerge over a range of coupling strengths. We analyse this phenomenon analytically for systems of linear oscillators, where we identify simple cases exhibiting exact synchronisation--up to a constant amplitude factor. Numerical simulations of nonlinear chaotic systems reveal stable forms of approximate anticipated synchronisation.

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David Ortiz del Campo, Tobias Galla, Raúl Toral. 2026-03-03. Anticipated synchronization in systems with distributed delay. https://arxiv.org/abs/2603.02918

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