Synchronization of laminar chaos

A new type of chaos is discovered recently (Muller et al. in Phys Rev Lett 120:084102, 2018), namely the laminar chaos that is exhibited by time-varying-time-delay systems. Unlike conventional chaos, the laminar chaos is unique in the sense that it has chaotically varying laminar phases that is periodically interrupted by irregular bursts. In this paper, for the first time, we explore the synchronization behavior of laminar chaos. We show that depending upon the choice of time delays the system exhibits transitions from generalized lag synchronization to generalized anticipatory synchronization through complete synchronization. If we introduce parameter mismatch in the frequency part of time varying delay, remarkably, it is observed that the oscillators synchronize for odd harmonic frequency mismatch. Further, interestingly, a mismatch in the amplitude of the time varying delay gives rise to either generalized lag or anticipatory synchronization. Most of the observed behaviors do not have any analog in the synchronization of normal chaos. These results will shed light on the understanding of the emergent behavior of laminar chaos and time-varying-time-delay systems.

Automated summary

In this paper, the authors investigate the synchronization behavior of laminar chaos and discover different synchronization modes depending on the choice of time delays. Interesting phenomena are observed by introducing parameter mismatches in the frequency and amplitude parts of the time-varying delay. These findings provide insights into the emergent behavior of laminar chaos and time-varying-time-delay systems.