Suppression and generation of rhythms in conjugately coupled nonlinear systems

Abstract

We explore two diametrically opposite phenomena provoked by conjugate coupling in nonlinear systems. The first effect, known as amplitude death, is observed when the two uncoupled systems are located in the oscillatory regime. In the presence of an appropriate coupling term the oscillatory behavior in both the systems vanishes. This amplitude death is found to persist for nonidentical oscillators, exhibiting different dynamics. In contrast, when the two uncoupled systems are located in the quiescent domain (fixed point behavior), suitable conjugate coupling seems to be capable of generating rhythms in the two systems. Similar to its amplitude death counterpart, induction of rhythms/oscillations is also observed for nonidentical systems. We demonstrate the phenomenon of amplitude death and oscillation generation by numerically studying two different systems, namely, an electrochemical corrosion model and the Hodgkin-Huxley model for neuronal spiking.