# Numerical and Experimental Studies of Self-Synchronization and Synchronized Chaos

### M. de Sousa Vieira, P. Khoury, Allan J. Lichtenberg, Michael A. Lieberman, W. Wonchoba, J. Gullicksen, J.Y. Huang, R. Sherman and M. Steinberg

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M92/5

1992

We study self-synchronization of digital phase-locked loops (DPLL's) and the chaotic synchronization of DPLL's in a communization system which consists of three or more coupled DPLL's. Triangular wave signals, convenient for experiments, are employed. Numerical and experimental studies of two loops are in good agreement, giving bifurcation diagrams that show quasiperiodic, locked, and chaotic behavior. The approach to chaos does not show the full bifurcation sequence of sinusoidal signals. For studying synchronization to a chaotic signal the chaotic carrier is generated in a subsystem of two or more self-synchronized DPLL's, where one of the loops is stable and the other is unstable, i.e. their Liapunov exponents are negative and positive, respectively. The receiver consists of a stable loop. We verified numerically and experimentally that the receiver synchronizes with the transmitter if the stable loop in the transmitter and receiver are nearly identical and the synchronization degrades with noise and parameter variation. We studied the phase space where synchronization occurs, and quantify the deviation from synchronization using the concept of mutual information. Permanent address: Electrical Engineering Department, San Jose State University, San Jose, CA 95192.

BibTeX citation:

@techreport{de Sousa Vieira:M92/5, Author = {de Sousa Vieira, M. and Khoury, P. and Lichtenberg, Allan J. and Lieberman, Michael A. and Wonchoba, W. and Gullicksen, J. and Huang, J.Y. and Sherman, R. and Steinberg, M.}, Title = {Numerical and Experimental Studies of Self-Synchronization and Synchronized Chaos}, Institution = {EECS Department, University of California, Berkeley}, Year = {1992}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/1929.html}, Number = {UCB/ERL M92/5}, Abstract = {We study self-synchronization of digital phase-locked loops (DPLL's) and the chaotic synchronization of DPLL's in a communization system which consists of three or more coupled DPLL's. Triangular wave signals, convenient for experiments, are employed. Numerical and experimental studies of two loops are in good agreement, giving bifurcation diagrams that show quasiperiodic, locked, and chaotic behavior. The approach to chaos does not show the full bifurcation sequence of sinusoidal signals. For studying synchronization to a chaotic signal the chaotic carrier is generated in a subsystem of two or more self-synchronized DPLL's, where one of the loops is stable and the other is unstable, i.e. their Liapunov exponents are negative and positive, respectively. The receiver consists of a stable loop. We verified numerically and experimentally that the receiver synchronizes with the transmitter if the stable loop in the transmitter and receiver are nearly identical and the synchronization degrades with noise and parameter variation. We studied the phase space where synchronization occurs, and quantify the deviation from synchronization using the concept of mutual information. Permanent address: Electrical Engineering Department, San Jose State University, San Jose, CA 95192.} }

EndNote citation:

%0 Report %A de Sousa Vieira, M. %A Khoury, P. %A Lichtenberg, Allan J. %A Lieberman, Michael A. %A Wonchoba, W. %A Gullicksen, J. %A Huang, J.Y. %A Sherman, R. %A Steinberg, M. %T Numerical and Experimental Studies of Self-Synchronization and Synchronized Chaos %I EECS Department, University of California, Berkeley %D 1992 %@ UCB/ERL M92/5 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/1929.html %F de Sousa Vieira:M92/5