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“Multiscroll Chaotic Oscillators Design in 1D, 2D 3D: Analysis, Theory and Applications ”

“Multiscroll Chaotic Oscillators Design in 1D, 2D 3D: Analysis, Theory and Applications ”. By: Dr. Carlos Sánchez-López. Autonomous University of Tlaxcala, Mexico Department of Electronics. Outline. What is Chaos? Previous Work Design of Chaotic Oscillators in 1D

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“Multiscroll Chaotic Oscillators Design in 1D, 2D 3D: Analysis, Theory and Applications ”

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  1. “Multiscroll Chaotic Oscillators Design in 1D, 2D 3D: Analysis, Theory and Applications” By: Dr. Carlos Sánchez-López Autonomous University of Tlaxcala, Mexico Department of Electronics

  2. Outline • What is Chaos? • Previous Work • Design of Chaotic Oscillators in 1D • Analysis, Simulation and Experimental results • Design of Chaotic Oscillators in 2D • Analysis, Simulation and Experimental results • Design of Chaotic Oscillators in 3D • Analysis and Numeric Simulations • Applications

  3. What is Chaos? • Chaotic oscillators can be used in various applications such as medicine, biology, communications system, etc. • Traditionally, the nonlinear resistor is made with OPAMP, CFOA, CCII, OTA as the principally block. Block Transmitter M-DCSK

  4. Previous Work • Chua´s circuit descomposition: a systematic design approach for chaotic oscillators. A.S. Elwakil, M.P. Kennedy, Journal of the Franklin Institute, pp. 251-265, February 2000. • On Current Feedback Operational Amplifier-Based Realizations of Chua´s Circuit. Recai Kilic, Circuits Systems Signal Processing,Vol. 22 No. 5 2003, pag. 475-491. • An Improved Chua’s Circuit and Its Use in Hyperchaotic CircuitGaurav Gandhi, Analog Integrated Circuits and Signal Processing, Vol. 46, pag. 173-178, 2006. • Improved implementation of Chua´s Chaotic Oscillator using Current Feedback Opamp. A.S. Elwakil and M.P. Kennedy, IEEE Transactions on Circuits and Systems I, Vol. 47 No 1 January 2000. • Inductorless Realization of Chua Oscillator O. Morgul, ELECTRONICS LETTERS, 17th August 1995, Vol 31, No 17.

  5. Chua’s Circuit α=10, β=14.87, m0=-0.68, m1=-1.27, the system produces a double-scroll chaotic attractors Cruz, J.M. Chua, L.O. [1993] “A CMOS IC nonlinear resistor for Chua's circuit,” IEEE Trans. Circuits Syst.-I 39, 985-995.

  6. Chua’s Circuit: Nonlinear resistor with Opamp Kennedy M.P. [1992] “Robust Opamp Realization of Chus’a Circuit,”Frequenz, vol. 46, no.3-4, pp. 66-80

  7. Nonlinear resistor with CFOA Elwakil [2000] “Chua’s circuit descomposition: a systematic design approach for chaotic oscillators,” Elsevier, pp. 251-265

  8. Nonlinear resistor with CCII Gandhi G. [2006] “An improved Chua’s Circuit and Its use in Hyperchaotic Circuit” Analog Integrated Circuits and Signal Processing, 46, 173-178

  9. Nonlinear Resistor with UGCs Sanchez, et.al. [2007] “Low-Voltage Chaotic Oscillator Using Voltage and Current Followers,” IEEE CERMA pp. 159-163.

  10. Grounded Inductor with UGCs Sanchez, et.al. [2008] “Simulation of Chua’s Chaotic Oscillator Using Unity-Gain Cells” IEEE ICCDCS, Cancun Mexico..

  11. CFOA Connected as UGCs Zin=∞ Zout=0 Zout=∞ Zin=0

  12. Nonlinear Resistor with UGC

  13. Nonlinear Resistor with UGCs

  14. Experimental and Simulation Results

  15. Experimental and Simulation Results Sanchez, et.al. [2008] “Experimental Verification of the Chua’s Circuit Designed with UGCs” IEICE Electron. Express, vol. 5, no. 17, pp. 657-661

  16. 1D-Multi-scroll Chaotic Oscillator: Analysis, Simulation and Experimental Results

  17. 1D Multi-scroll Chaotic Oscillator • Attractors via PWL Functions. • Generalized Chua’s circuit. • Sine Function Approach • Nonlinear Transconductor Method • Cubic Function • Piecewise-quadratic Function. • Saturated Functions. • Hysteresis series method. • Sawtooth Function.

  18. f(vc1)=h1vc1+h2v3c1 f(vc1)=pvc1+qvc1|vc1|

  19. Transconductor no-lineal

  20. Saturated Functions

  21. Saturated Functions

  22. Saturated Functions

  23. Saturated Functions

  24. Saturated Functions

  25. 2D-Multi-scroll Chaotic Oscillator: Analysis, Simulation and Experimental Results

  26. Saturated Functions

  27. Saturated Functions with CCII+

  28. Saturated Functions

  29. Generalized Chua’s Circuit

  30. Generalized Chua’s Circuit

  31. Generalized Chua’s Circuit

  32. 3D-Multi-scroll Chaotic Oscillator: Analysis and Numeric Simulation

  33. Saturated Functions

  34. Saturated Functions

  35. Saturated Functions

  36. Applications to Secure Communications

  37. Applications

  38. Applications: Duffing and Chua’s Systems

  39. Applications Transmitter Receiver Synchronization Circuit

  40. Applications

  41. Thanks you for your attention

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