Chimeras in digital phase-locked loops.

Area of Science:

• Nonlinear dynamics
• Complex systems
• Network science

Background:

• Digital phase-locked loops (DPLLs) are crucial nonlinear feedback systems in electronics.
• Existing research often focuses on isolated DPLL units, neglecting coupled network behavior.
• DPLLs commonly operate in coupled modes in real-world applications.

Purpose of the Study:

• To investigate the collective dynamics of one- and two-dimensional DPLL networks with nonlocal coupling.
• To identify and characterize emergent spatiotemporal structures, particularly chimera patterns.
• To explore the conditions for stable phase-locked states and the emergence of complex dynamics.

Main Methods:

• Analytical derivation of the stable phase-locked state's parametric zone for 1D networks.
• Numerical simulation and analysis of 1D and 2D DPLL networks under nonlocal coupling.
• Characterization of chimera patterns using local curvature and correlation functions.

Main Results:

• Analytical identification of the stable phase-locked regime in 1D DPLL networks.
• Observation of diverse spatiotemporal structures, including chimera patterns, in 1D networks.
• Identification of various chimera patterns (e.g., strip, spot) in 2D DPLL networks.

Conclusions:

• Chimera patterns exist in widely used engineering systems like DPLL networks.
• The findings suggest that chimera patterns in DPLL networks are experimentally observable.
• This research expands the understanding of complex dynamics in coupled nonlinear systems.