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United States Patent 
Pecora et al.
 CASCADING SYNCHRONIZED CHAOTIC SYSTEMS
 Inventors: Louis M. Pecora; Thomas L. Carroll, both of Alexandria, Va.
 Assignee: The United States of America as
represented by the Secretary of the Navy, Washington, D.C.
 Appl. No.: 129,495
 Filed: Sep. 30,1993
 Int. Cl.« H03B 29/00; G06F 1/02
 U.S. CI. 380/48; 380/9;
380/46; 331/78; 364/717
 Field of Search 331/78; 364/717; 380/9,
380/46, 48, 49, 50
 References Cited
U.S. PATENT DOCUMENTS
5,007,087 4/1991 Bernstein et al 380/46
5,245,660 9/1993 Pecora et al 380/48
5,291,555 3/1994 Cuomo et al 380/48 X
K. Murali and M. Lakshmanan, "Transmission of Signals by Synchronization in a chaotic Van der Pol-Duffing Oscillator", Physical Review E, vol. 48, No. 3, Sep., 1993, pp. R1624-R1626.
James P. Crutchfield et al., "Chaos", Dec. 1986, pp. 46-57, Scientific American.
Louis M. Pecora and Thomas L. Carroll, "Synchronization in Chaotic Systems", Physical Review Letters, vol. 64, No. 8, Feb. 19, 1990, pp. 821-824. Louis M. Pecora and Thomas L. Carroll, "Driving systems with chaotic signals", Physical Review A, vol. 44, No. 4, Aug. 15, 1991, pp. 2374-2383. Thomas L. Carroll and Louis N. Pecora, "Synchronizing Chaotic Circuits", IEEE Transactions on Circuits and Systems, vol. 38, No. 4, Apr. 1991, pp. 453^56. Lou Pecora and Tom Carroll, "Synchronized Chaotic Signals and Systems", Proceedings of ICASSP Conference, San Francisco, Calif., Mar. 1992.
[ii] Patent Number: 5,379,346  Date of Patent: Jan. 3, 1995
Alan V. Oppenheim et al., "Signal Processing in the Context of Chaotic Signals", IEEE International Conference, San Francisco, Calif., Mar. 1992. T. L. Carroll and L. M. Pecora, "A Circuit For Studying The Synchronization of Chaotic Systems", International Journal of Bifurcation and Chaos, vol. 2, No. 3, Published Dec. 4, 1992, pp. 659-667.
(List continued on next page.)
Primary Examiner—Bernarr E. Gregory
Attorney, Agent, or Firm—Daniel Kalish; Thomas E.
A cascaded synchronized nonlinear system includes a . nonlinear transmitter having stable first and second subparts. The first subpart produces a first transmitter signal for driving the second subpart and the second ; subpart produces a second transmitter signal for driving the first subpart. The nonlinear transmitter transmits the second transmitter signal to a nonlinear cascaded receiver. The receiver, being for producing an output signal in synchronization with the second transmitter signal, includes a first stage (a duplicate of the first subpart) responsive to the second transmitter signal for producing a first receiver signal. The receiver further includes a second stage (a duplicate of the second subpart) responsive to the first receiver signal for producing the output signal. The cascaded synchronized nonlinear system can be used in an information transfer system. The transmitter, responsive to an information signal produces a drive signal for transmission to the receiver. An error detector compares the drive signal and the output signal produced by the receiver to produce an error signal indicative of the information contained in the information signal.
36 Claims, 26 Drawing Sheets
L. J. Kocarev et al., "Experimental Demonstration of Secure Communications Via Chaotic Synchronization", International Journal of Bifurcation and Chaos, vol. 2, No. 3, Published Dec. 4, 1992, pp. 709-713. U. Parlitz et al., "Transmission of Digital Signals By Chaotic Synchronization", International Journal of Bifurcation and Chaos, vol. 2, No. 4, (1992) 973-977. Kevin M. Cuomo and Alan V. Oppenheim, "Circuit Implementation of Synchronized Chaos With Applications to Communications", Physical Review Letters, vol. 71, No. 1, Jul. 5, 1993, pp. 65-68. William L. Ditto and Louis M. Pecora, "Mastering
Chaos", Scientific American, Aug. 1993, vol. 269, No. 2, pp. 78-84. ~~
Joseph Neff and Thomas L. Carroll, "Circuits That Get Chaos in Sync", Scientific American, Aug. 1993, pp. 120-122.
Thomas L. Carroll and Louis M. Pecora, "Communicating with Chaos", 1993 NRL Review, pp. 75-82. T. L. Carroll and L. M. Pecora, "Cascading Synchronized Chaotic Systems", Physica D, vol. 67, 1993, pp. 126-140.
U.S. application Ser. No. 07/880,789, filed May 11,1992 Pecora et al., assigned by the United States Government.