Eur. Phys. J. Plus (2022) 137: 561
https://doi.org/10.1140/epjp/s13360-022-02778-5

Regular Article

Synchronization of laminar chaos

¹ Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, 713 104, Burdwan, West Bengal, India
² Department of Physics, Bankura University, 722 155, Bankura, West Bengal, India

^c tbanerjee@phys.buruniv.ac.in

Received: 4 April 2022
Accepted: 28 April 2022
Published online: 6 May 2022

Abstract

A new type of chaos is discovered recently (Müller 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.