Anticipated synchronization in systems with distributed delay

TL;DR

This paper extends the concept of anticipated synchronization to systems with distributed delay times, demonstrating that approximate anticipation can occur over a range of conditions, supported by analytical and numerical results.

Contribution

It introduces a framework for anticipated synchronization with distributed delays and analyzes both linear and nonlinear systems to show the emergence of approximate anticipation.

Findings

Approximate anticipated synchronization occurs over a range of coupling strengths.

Exact synchronization is possible in linear systems with specific delay distributions.

Numerical simulations show stable approximate anticipation in nonlinear chaotic systems.

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.