Cascading synchronized chaotic systems

• US 5,379,346 A
• Filed: 09/30/1993
• Issued: 01/03/1995
• Est. Priority Date: 09/30/1993
• Status: Expired due to Fees

• Current Assignee: The United States of America As Represented By The Secretary of Agriculture
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: Carroll, Thomas L., Pecora, Louis M.
• Primary Examiner(s): Gregory, Bernarr E.
• Application Number:
  US08/129,495
• Time in Patent Office: 460 Days
• Field of Search: 331/78, 364/717, 380/9, 380/46, 380/48, 380/49, 380/50
• US Class Current: 380/263
• CPC Class Codes: G06F 17/10 Complex mathematical operations function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544
• CPC Class Codes: G06G 7/26 Arbitrary function generators using Fourier series or other orthogonal functions G06G7/19; using curve followers G06K11/02
• CPC Class Codes: H03B 21/02 by plural beating, i.e. for frequency synthesis ; Beating in combination with multiplication or division of frequency digital frequency synthesis using a ROM G06F1/02; digital frequency synthesis in general H03K; indirect frequency synthesis using a PLL H03L7/16
• CPC Class Codes: H03B 29/00 Generation of noise currents and voltages gasfilled discharge tubes with solid cathode specially adapted as noise generators H01J17/005
• CPC Class Codes: H03B 5/20 with frequency-determining element comprising resistance and either capacitance or inductance, e.g. phase-shift oscillator
• CPC Class Codes: H04L 27/001 using chaotic signals for secret or secure communication H04L9/001

Abstract

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.

Claims

1. A cascaded synchronized nonlinear electrical system comprising:

(a) a nonlinear transmitter having stable first and second subparts, said first subpart producing a first transmitter signal for driving said second subpart, said second subpart producing a second transmitter signal for driving said first subpart, said nonlinear transmitter being for transmission of said second transmitter signal; and

(b) a nonlinear cascaded receiver responsive to said second transmitter signal transmitted by said transmitter, said receiver being for producing an output signal in synchronization with said second transmitter signal, said receiver comprising a first stage responsive to said second transmitter signal for producing a first receiver signal, said first stage being a duplicate of said first subpart, and said receiver further comprising a second stage responsive to said first receiver signal for producing said output signal, said second stage being a duplicate of said second subpart.

2. The system of claim 1 wherein said first stage produces said first receiver signal in synchronization with said first transmitter signal.

3. The system of claim 1 wherein said transmitter comprises a non-Lorenz system.

4. The system of claim 3 wherein said transmitter comprises a non-Chua circuit.

5. The system of claim 1 wherein said transmitter comprises a non-Chua circuit.

6. The system of claim 1, wherein at least part of said first subpart of element (a) is external to said second subpart of element (a), and at least part of said second subpart of element (a) is external to said first subpart of element (a).

7. An electrical information transfer system comprising:

(a) a nonlinear transmitter responsive to an information signal for producing a drive signal, said transmitter having stable first and second subparts, said first subpart producing a first transmitter signal for driving said second subpart, said second subpart producing a second transmitter signal for driving said first subpart, said nonlinear transmitter being responsive to said second transmitter signal for transmission of said drive signal; and

(b) a nonlinear cascaded receiver responsive to said drive signal, said receiver comprising a first stage responsive to said drive signal for producing a first receiver signal, said first stage being a duplicate of said first subpart, and said receiver further comprising a second stage responsive to said first receiver signal for producing an output signal, said second stage being a duplicate of said second subpart; and

(c) an error detector coupled to said receiver being responsive to said drive signal and to said output signal for producing an error signal indicative of the information contained in said information signal.

8. The system of claim 7 wherein said transmitter comprises a non-Lorenz system.

9. The system of claim 8 wherein said transmitter comprises a non-Chua circuit.

10. The system of claim 7 wherein said transmitter comprises a non-Chua circuit.

11. The system of claim 7 wherein said transmitter comprises a modulator responsive to said second transmitter signal and to said information signal for producing said drive signal.

12. The system of claim 11 wherein said modulator is a nonlinear modulator.

13. The system of claim 7 wherein said transmitter further comprises means responsive to said information signal for varying the value of a transmitter parameter.

14. The system of claim 13 further comprising means responsive to said error signal for varying the value of a receiver parameter corresponding to said transmitter parameter so that the variation of said receiver parameter is in synchronization with the variation of said transmitter parameter.

15. A synchronized electrical system, comprising:

a nonlinear dynamic drive system for producing a drive signal and transmitting the drive signal, the drive system having at least two stable subsystems; and

a cascaded nonlinear driven system responsive to said drive system to receive the drive signal and comprising cascade connected subsystems of the driven system, said driven system subsystems being substantially duplicates of said at least two drive system subsystems, said at least two driven subsystems comprising a first subsystem responsive to the drive signal and a second subsystem for producing an output signal in synchronization with the drive signal.

16. A system as recited in claim 15, wherein said drive system produces a first signal to be synchronized and said driven system reproduces the first signal.

17. The system of claim 15, wherein said driven system comprises a non-Lorenz device.

18. A synchronized electrical system, comprising:

a nonlinear dynamic drive system for producing a dynamic drive signal and having at least a first and a second interdependent and stable subsystem for producing a first signal to be synchronized; and

a nonlinear dynamic driven system coupled to said drive system and receiving the drive signal, said driven system comprising;

a first driven subsystem comprising a duplicate of said first subsystem of said drive system, said first driven subsystem being interdependent to synchronize and reproduce the first signal; and

a second subsystem comprising a duplicate of said second subsystem of said drive system, said second driven subsystem being connected to the first driven subsystem and being responsive thereto to receive the reproduced signal and being interdependent to synchronize and reproduce the drive signal.

19. The system of claim 18, further comprising a comparator for comparing the drive signal and the reproduced drive signal to confirm synchronization.

20. A method of synchronizing, comprising the steps of:

(a) electrically producing a drive value and a first value to be matched using a differential equation model;

(b) broadcasting the drive value to a receiver; and

(c) electrically producing in the receiver an output value and a receiver first value in synchronization with the drive value and the first value, respectively, by using the drive value received and at least a pair of stable differential equation model subsystems which are subsets of the equation model, wherein said pair of differential equation model subsystems includes at least one common variable, said pair of differential equation model subsystems comprising a first subsystem dependent on the drive value for producing the receiver first value and a second subsystem dependent on the receiver first value for producing the output value.

21. A method as recited in claim 20, further comprising comparing the drive value and the reproduced drive value to confirm matching of the first value and the reproduced first value.

22. An electrical information transfer system, comprising:

a transmitter having at least two stable subsystems for producing a dynamic drive signal carrying an information signal; and

a cascaded receiver coupled to said transmitter to receive the drive signal and comprising;

cascade connected subsystems of the receiver, said receiver subsystems being substantially duplicates of said at least two transmitter subsystems for producing a reproduced signal comprising the drive signal with the information signal removed; and

a combining circuit for combining the dynamic drive signal and the reproduced signal to reproduce the information signal.

23. The system of claim 22, wherein said combining circuit comprises a nonlinear device.

24. A system as recited in claim 22, wherein said transmitter comprises a drive system producing a drive signal and an adder combining the drive signal and the information signal to produce the dynamic drive signal carrying the information signal.

25. A system as recited in claim 22, wherein said combining circuit is an error detector.

26. The system of claim 22, wherein said transmitter comprises a drive system for producing a drive signal and a nonlinear combining circuit for combining the drive signal and the information signal to produce the dynamic drive signal.

27. A method of transferring information, comprising the steps of:

(a) electrically producing drive value using a differential equation model;

(b) combining the drive value with an information value to produce a broadcast value;

(c) broadcasting the broadcast value to a receiver;

(d) electrically reproducing the drive value in the receiver from the broadcast value and at least a pair of stable differential equation model subsystems which includes subsets of the equation model, wherein said pair of differential equation model subsystems includes at least one common variable; and

(e) combining the reproduced drive value with the broadcast value to reproduce the information value.

28. A method as recited in claim 27, wherein step (b) comprises adding the drive value and the information value and step (e) comprises subtracting the reproduced drive value from the broadcast value.

29. An electrical information transfer system, comprising:

a transmitter including a parameter and having at least two stable subsystems, said transmitter being for producing a dynamic drive signal carrying an information signal produced by parameter variations; and

a cascaded receiver coupled to said transmitter to receive the drive signal and comprising;

cascade connected subsystems of the receiver, said receiver subsystems being substantially duplicates of said at least two transmitter subsystems for producing a reproduced signal comprising the drive signal with the information signal removed; and

a combining circuit combining the drive signal and the reproduced signal to produce a parameter difference signal indicating variations in the parameter.

30. A system as recited in claim 29, wherein the receiver includes a fixed parameter.

31. A system as recited in claim 30, wherein said combining circuit comprises an error detector.

32. A method of information transfer, comprising the steps of:

(a) electrically producing a drive value using a differential equation model with a varied equation parameter varied responsive to an information value;

(b) broadcasting the drive value to a receiver;

(c) electrically reproducing the drive value in the receiver from the broadcast drive value and at least a pair of stable differential equation model subsystems which are subsets of the equation model, wherein said pair of differential equation model subsystems includes at least one common variable with the parameter fixed; and

(d) combining the reproduced drive value with the broadcast drive value to produce a parameter change value corresponding to the information value.

33. A method as recited in claim 32, wherein step (a) comprises changing the parameter between two values and the parameter change value changes between a pair of values.

34. An electrical information transfer system, comprising:

a transmitter including a parameter having at least two stable subsystems for producing a dynamic drive signal carrying an information signal produced by parameter variation; and

a cascaded receiver coupled to said transmitter to receive the drive signal and comprising;

cascade connected subsystems of the receiver, including the parameter said receiver subsystems being substantially duplicates of said at least two transmitter subsystems and being for producing a reproduced signal comprising the drive signal with the information signal removed;

a combining circuit combining the drive signal and the reproduced signal to produce a parameter error signal; and

a parameter change circuit changing the parameter of the receiver to match the parameter variation of said transmitter to reproduce the information signal responsive to the parameter error signal.

35. A system as recited in claim 34, wherein said combining circuit comprises an error detection circuit and said parameter change circuit performs stepwise matching of the parameter variation.

36. A method of transferring information, comprising the steps of:

(a) electrically producing a drive value using a source differential equation model with a varied equation parameter varied responsive to an information value;

(b) broadcasting the drive value to a receiver;

(c) electrically reproducing the drive value in the receiver from the broadcast value and at least a pair of stable differential equation model subsystems which are subsets of the equation model, wherein said pair of differential equation model subsystems includes at least one common variable and which includes the parameter;

(d) combining the reproduced drive value with the broadcast value to produce a parameter error; and

(e) changing the parameter of the differential equation subsystems responsive to the parameter error.