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Anticipated synchronization in systems with distributed delay

Author

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  • Ortiz del Campo, David
  • Galla, Tobias
  • Toral, Raúl

Abstract

Anticipated synchronization occurs when a driven dynamical system synchronizes 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 synchronization can emerge over a range of coupling strengths. We analyse this phenomenon analytically for systems of linear oscillators, where we identify simple cases exhibiting projective anticipated synchronization, i.e., regimes in which the state of the driven system reproduces a time-advanced version of the driver up to a multiplicative amplitude factor. Numerical simulations of nonlinear chaotic systems reveal stable forms of approximate anticipated synchronization.

Suggested Citation

  • Ortiz del Campo, David & Galla, Tobias & Toral, Raúl, 2026. "Anticipated synchronization in systems with distributed delay," Chaos, Solitons & Fractals, Elsevier, vol. 208(P4).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p4:s0960077926005011
    DOI: 10.1016/j.chaos.2026.118360
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