Dynamical effects of integrative time-delay coupling

We study coupled dynamical systems wherein the influence of one system on the other is cumulative: coupling signals are integrated over a time interval tau. A major consequence of integrative coupling is that amplitude death occurs over a wider range and in a single region in parameter space. For coupled limit cycle oscillators (the Landau-Stuart model) we obtain an analytic estimate for the boundary of this region while for coupled chaotic Lorenz oscillators numerical results are presented. For given tau we find that there is a critical coupling strength at which the frequency of oscillations changes discontinuously.