For the model of a Closed Phase Locked Loop (CPLL) communication System consists of both the transmission and receiver ends. This model is considered to be in a multi-order intermittent chaotic state. The chaotic signals are then synchronized along side with our system. This chaotic synchronization will be demonstrated and furthermore, a modulation will be formed to examine the system if it will perfectly reconstruct or not. Finally we will demonstrate the synchronization conditions of the system.
References
[1]
Carroll, T.L. and Pecora, L.M. (1998) Synchronizing Hyperchaotic Volume-Preserving Maps and Circuits. IEEE Transactions on Circuits and Systems I-regular Papers, 45, 656-659. https://doi.org/10.1109/81.678482
[2]
Pecora, L.M. and Carrol, L. (1990) Synchronization in Chaotic Systems. Physical Review Letters, 64, 821-824. https://doi.org/10.1103/PhysRevLett.64.821
[3]
Pecora, L.M. and Carrol, T.L. (1991) Synchronizing Chaotic Circuits. IEEE Transactions on Circuits and Systems, 38, 453-456. https://doi.org/10.1109/31.75404
[4]
Endo, T. and Chua, L.O. (1991) Synchronization of Chaos in Phase-Locked Loops. IEEE Transactions on Circuits and Systems, 38, 1580-1588. https://doi.org/10.1109/31.108517
[5]
Harb, A. and Zohdy, M. (2002) Synchronization of Chaotic Systems Applied to Communications Systems. Conference Paper.
[6]
Sato, A. and Endo, T. (1995) Experiments of Scure Communications via Chaotic Synchroniztion of Phase-Locked Loops. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E78, 1286-1290.
[7]
Carroll, T.L., Johnson, G.A. and Pecora, L.M. (1999) Parameter-Insensitive and Narrow-Band Synchronization of Chaotic Circuits. International Journal of Bifurcation and Chaos, 9, 2189-2196. https://doi.org/10.1142/S0218127499001619
[8]
Wu, S. (1987) Chua’s Circuit Family. Proceedings of the IEEE, 75, 1022-1032. https://doi.org/10.1109/PROC.1987.13847
[9]
Salam, F. and Sastry, S. (1985) Dynamics of the Forced Josephson Junction Circuit: The Region of Chaos. IEEE Transactions on Circuit and Systems, 32, 784-796.
[10]
Kennedy, M.P. and Chua, L.O. (1981) Van der Pol and chaos. IEEE Transactions on Circuits and Systems, 33, 974-980. https://doi.org/10.1109/TCS.1986.1085855
[11]
Endo, T. and Chua, L.O. (1988) Chaos from Phase-Locked Loops. IEEE Transactions on Circuits and Systems, 35, 987-1003. https://doi.org/10.1109/31.1845
[12]
Watada, K., Endo, T. and Seishi, H. (1998) Shilnikov Orbits in an Autonomous Third-Order Chaotic Phase-Locked Loop. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45, 979-983. https://doi.org/10.1109/81.721264
[13]
Harb, B. and Harb, A. (2003) Chaos and Bifurcation in Third-Order Phase Locked Loop. Proceedings of the 35th Southeastern Symposium on System Theory, Morgantown, WV, 18-18 March 2003. https://doi.org/10.1109/SSST.2003.1194549
[14]
Harb, A., Zaher, A. and Zohdy, M. (2002) Nonlinear Recursive Backstepping Chaos Control, ACC-Alaska.
[15]
Frey, D.R. (1993) Chaotic Digital Encoding: An Approach to Secure Communications. IEEE Transactions on Circuits and Systems, 40, 660-666. https://doi.org/10.1109/82.246168
[16]
Jackson, E.A. (1991) Control of Dynamic Flows with Attractors. Physical Review A, 44, 4839-4853. https://doi.org/10.1103/PhysRevA.44.4839
