Amplitude death in the absence of time delays in identical coupled oscillators

Abstract

We study the dynamics of oscillators that are mutually coupled via dissimilar (or "conjugate") variables and find that this form of coupling leads to a regime of amplitude death. Analytic estimates are obtained for coupled Landau-Stuart oscillators, and this is supplemented by numerics for this system as well as for coupled Lorenz oscillators. Time delay does not appear to be necessary to cause amplitude death when conjugate variables are employed in coupling identical systems. Coupled chaotic oscillators also show multistability prior to amplitude death, and the basins of the coexisting attractors appear to be riddled. This behavior is quantified: an appropriately defined uncertainty exponent in the coupled Lorenz system is shown to be zero.