Route to chaos in a third-order phase-locked loop network

Signal Processing

Volumn 89, Issue 8, 2009, Pages 1678-1682

  Monteiro, L H A ^a,b   Lisboa, A C ^b   Eisencraft, M ^a,b  

^a MACKENZIE PRESBYTERIAN UNIVERSITY   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Chaos; Hopf bifurcation; Period doubling bifurcation; Phase locked loop; Saddle saddle bifurcation; Synchronism

Indexed keywords

CHAOS; PERIOD-DOUBLING BIFURCATION; PHASE-LOCKED LOOP; SADDLE-SADDLE BIFURCATION; SYNCHRONISM;

CHAOTIC SYSTEMS; COMMUNICATION SYSTEMS; DELAY CIRCUITS; PHASE LOCKED LOOPS; SPURIOUS SIGNAL NOISE; TELECOMMUNICATION NETWORKS;

HOPF BIFURCATION;

EID: 64749109972     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2009.03.006     Document Type: Article

References (24)

1. Best R.E. Phase-locked Loops: Design, Simulation, and Applications (2003), McGraw-Hill, New York
2. Gardner F.M. Phaselock Techniques (2005), Wiley, New York
3. Piqueira J.R.C., and Monteiro L.H.A. Considering second-harmonic terms in the operation of the phase detector for second-order phase-locked loop. IEEE Transactions on Circuits and Systems I 50 6 (2003) 805-809
4. Monteiro L.H.A., Favaretto Filho D.N., and Piqueira J.R.C. Bifurcation analysis for third-order phase-locked loops. IEEE Signal Processing Letters 11 5 (2004) 494-496
5. Piqueira J.R.C., Takada E.Y., and Monteiro L.H.A. Analyzing the effect of the phase-jitter in the operation of second-order phase-locked loops. IEEE Transactions on Circuits and Systems II 52 6 (2005) 331-335
6. Piqueira J.R.C., and Monteiro L.H.A. All-pole phase locked-loops: calculating lock-in range by using Evan's root-locus. International Journal of Control 79 7 (2006) 822-829
7. Watada K., Endo T., and Seishi H. Shilnikov orbits in an autonomous third-order chaotic phase-locked loop. IEEE Transactions on Circuits and Systems I 45 9 (1998) 979-983
8. Harb B.A., and Harb A.M. Chaos and bifurcation in a third-order phase locked loop. Chaos, Solitons and Fractals 19 3 (2004) 667-672
9. Matsumoto T. A chaotic attractor from Chua's circuit. IEEE Transactions on Circuits and Systems 31 12 (1984) 1055-1058
10. Endo T., and Chua L.O. Chaos from phase-locked loops. IEEE Transactions on Circuits and Systems 35 8 (1988) 987-1003
11. M.P. Kennedy, R. Rovatti, G. Setti (Eds.), Chaotic Electronics in Telecommunications, CRC Press, Boca Raton (Florida), 2000.
12. L.E. Larson, J.M. Liu, L.S. Tsimring (Eds.), Digital Communications Using Chaos and Nonlinear Dynamics, Springer, New York, 2006.
13. Y. J. Zhang (Ed.), Advances in Image and Video Segmentation, Springer, New York, 2006.
14. Wu C.W. Synchronization in Coupled Chaotic Circuits and Systems (2002), World Scientific, New Jersey
15. Monteiro L.H.A., Santos R.V., and Piqueira J.R.C. Estimating the critical number of slaves nodes in a single-chain PLL network. IEEE Communications Letters 7 9 (2003) 449-450
16. Monteiro L.H.A., Canto N.C.F., Chauí-Berlinck J.G., Orsatti F.M., and Piqueira J.R.C. Global and partial synchronism in phase-locked loop networks. IEEE Transactions on Neural Networks 14 6 (2003) 1572-1575
17. M.K.S. Kunyosi, L.H.A. Monteiro, Recognition of Noisy Images by PLL Networks, Signal Processing 89 (7) (2009) 1311-1319.
18. Piqueira J.R.C., Marmo C.N., and Monteiro L.H.A. Using central manifold theorem in the analysis of master-slave synchronization networks. Journal of Communications and Networks 6 3 (2004) 1-6
19. Piqueira J.R.C., Castillo-Vargas S.A., and Monteiro L.H.A. Two-way master-slave double-chain networks: limitations imposed by linear master drift for second-order PLLs as slave nodes. IEEE Communications Letters 9 9 (2005) 829-831
20. Piqueira J.R.C., and Freschi M.C. Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks. AEU International Journal of Electronics and Communications 62 6 (2008) 459-463
21. Guckenheimer J., and Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (2002), Springer, New York
22. Ogata K. Modern Control Engineering (2001), Prentice-Hall, New York
23. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from a time series. Physica D 16 3 (1985) 285-317
24. Kennedy M.P., and Kolumbán G. Digital communication using chaos. Signal Processing 80 7 (2000) 1307-1320