Chimeras in digital phase-locked loops

TL;DR

This paper investigates the emergence of chimera states in networks of digital phase-locked loops (DPLLs), revealing complex spatiotemporal patterns and stability conditions, with implications for electronic communication systems.

Contribution

It analytically and numerically explores chimera phenomena in coupled DPLLs, a novel application in engineering systems, and characterizes various chimera patterns in 1D and 2D networks.

Findings

Chimera states occur in coupled DPLLs under realistic nonlocal coupling.

Analytical derivation of stable phase-locked regions in 1D networks.

Identification of diverse chimera patterns like strip and spot chimeras.

Abstract

Digital phase-locked loops (DPLLs) are nonlinear feedback-controlled systems that are widely used in electronic communication and signal processing applications. In most of the applications they work in coupled mode, however, vast of the studies on DPLLs concentrate on the dynamics of a single isolated unit. In this paper we consider both one- and two-dimensional networks of DPLLs connected through a practically realistic nonlocal coupling and explore their collective dynamics. For the one-dimensional network we analytically derive the parametric zone of stable phase-locked state in which DPLLs essentially work in their normal mode of operation. We demonstrate that apart from the stable phase-locked state, a variety of spatiotemporal structures including chimeras arise in a broad parameter zone. For the two-dimensional network under nonlocal coupling we identify several variants of chimera patterns, such as strip and spot chimeras. We identify and characterize the chimera patterns through suitable measures like local curvature and correlation function. Our study reveals the existence of chimeras in a widely used engineering system, therefore, we believe that these chimera patterns can be observed in experiments as well.