Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system

We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication sy...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2014-03, Vol.24 (1), p.013116-013116
Main Authors: Banerjee, Tanmoy, Paul, Bishwajit, Sarkar, B. C.
Format: Article
Language:English
Subjects:
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Communications systems
Computer simulation
COMPUTERIZED SIMULATION
CORRELATION FUNCTIONS
COUPLING
Electric communication systems
ENGINEERING
Mathematical models
MATHEMATICAL SOLUTIONS
Nonlinear control
Nonlinear feedback
NONLINEAR PROBLEMS
Nonlinearity
Phase locked loops
RANDOMNESS
STABILITY
Stability analysis
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Summary:We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4863859