Skip to main content

Complex Dynamics and Cellular Neural Networks

  • Chapter
Book cover Soft Computing

Abstract

Artificial neural networks, fuzzy systems, and cellular neural networks are nonlinear systems. Furthermore, their use is directed towards the modeling and control of dynamic non-linear systems. Soft computing techniques would, in any case, be superfluous for studying linear systems, being more often than not dedicated to the study of systems having a certain degree of complexity. Hence the need to introduce the basic tools for analyzing complex dynamic systems. This chapter is therefore arranged around two themes: the first regards the analysis of complex dynamic systems, while the second deals with the processing of an innovative procedure for generating complex dynamics by means of CNNs and thus by means of soft computing types of techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. TS Parker, Chua LO. Practical Numerical Algorithms for Chaotic Systems. Springer-Verlag, 1989

    Book  MATH  Google Scholar 

  2. Eckmann JP, Ruelle D. Ergodic Theory of Chaos and Strange Attractors. Reviews of Modern Physics Part I. 1985; 57: 3

    Google Scholar 

  3. Thompson JMT, Stewart HB. Nonlinear Dynamics and Chaos. John Wiley and Sons, 1989

    Google Scholar 

  4. Lorenz EN. Deterministic Nonperiodic Flow. Journal Atmospheric Science. 1963; 20; 130

    Article  Google Scholar 

  5. Rasband SN. Chaotic Dynamics of Nonlinear Systems. John Wiley & Sons, 1990

    Google Scholar 

  6. Hasler MJ. Electrical Circuits with Chaotic Behavior. 1 Proceedings of the IEEE, Aug. 1987

    Google Scholar 

  7. Ikeda K. Chaotic Itinerancy. International Symposia on Information Sciences, Ilzuka, July 1992

    Google Scholar 

  8. Gleick J. Chaos: Making a New Science. Viking Press, 1987

    MATH  Google Scholar 

  9. Mayer-Kress G,. Choi I, Weber N, Bargar R, H’bler A. Music Signals from Chua’s Circuit. IEEE Transactions on Circuits and Systems II. 1993; 40

    Google Scholar 

  10. Heileman GL, Abdallah C, Hush D, Baglio S. Chaotic Probe Strategies in Open Addressing Hashing. 1993 International Symposium on Nonlinear Theory and its Applications, Hawaii, Dec, 1993

    Google Scholar 

  11. Chaos Simulator and Application to Washing Machine, GOLDSTAR, Tech. Rep., July 1993

    Google Scholar 

  12. Dedieu H, Kennedy MP, Hasler M. Chaos Shift Keying: Modulation and Demodulation of a Chaotic Character Using Self-Synchronizing Chua’s Circuits. IEEE Transactions on Circuits and Systems II. 1993; 40

    Google Scholar 

  13. Bamsley MF. Fractals Everywhere. Academic Press Professional, 1993

    Google Scholar 

  14. Guckenheimer J, Holmes P. Nonlinear Oscillation, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, 1983

    Google Scholar 

  15. Fornasini E, Marchesini G. Appunti di Teoria dei Sistemi. Edizioni Libreria Progetto, Padova, 1985

    Google Scholar 

  16. Oseledec VI. A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems. Trans. Moscow Math. Soc. 1968; 19: 97

    MathSciNet  Google Scholar 

  17. Haken H. At least One Lyapunov Exponent Vanishes if the Trajectory of an Attractor does not Contain a Fixed Point. Physics Letter. 1983; 94A(2): 71–72

    Article  MathSciNet  Google Scholar 

  18. Guillemin V, Pollack A. Differential Topology. Prentice-Hall, Englewood Cliffs 1974

    MATH  Google Scholar 

  19. Grassberger P, Procaccia I. Dimension and Entropies of Strange Attractors from a Fluctuating Dynamics Approach. Physica D. 1984; 13

    Google Scholar 

  20. Kaplan JL, Yorke JA. Chaotic Behavior of Multidimensional Difference Equations. Lecture Notes in Mathematics Springer-Verlag, 1979; 228–237

    Google Scholar 

  21. Badii R, Politi A. Statistical Description of Chaotic Attractors: The Dimension Function. Journal of Statistical Physics. 1985; 40(5/6): 725–750

    MathSciNet  MATH  Google Scholar 

  22. Mayer-Kress G. (editor). Dimension and Entropies in Chaotic Systems. Springer-Verlag, 1986

    Google Scholar 

  23. Arena P. Baglio S, Fortuna L, Manganaro G. State Controlled CNN: A New Strategy for Generating High Complex Dynamics. IEICE trans. On Fundamentals October 1996; E79-A: 10

    Google Scholar 

  24. Arena P, Baglio S, Fortuna L, Manganaro G. Chua’s Circuit can be Generated by CNN Cells. IEEE Trans. On Circuits and Systems-Part I. February 1995; 42: 2

    Google Scholar 

  25. Arena P. Baglio S, Fortuna L, Manganaro G. Generation of N-Double Scroll Via Cellular Neural Networks. Int. Journal of Circuit Theory and Application 1966; 24

    Google Scholar 

  26. Geiger RL, Allen PE, Strader NR. VLSI: Design Techniques for Analog and Digital Circuits. McGraw-Hill, 1990

    Google Scholar 

  27. Arena P, Baglio S, Fortuna L, Manganaro G. Experimental Signal Transmission Using Synchronised State Controlled Cellular Neural Networks. IEE Electronics Letters. 1996; 32: 362–363

    Article  Google Scholar 

  28. Caponetto R, Lavorgna M, Occhipinti L. Cellular Neural Networks in Secure Transmission Applications. 4th IEEE Int. Workshop on Cellular Neural Networks and their Appl.s, Seville, 1996; 411–416

    Google Scholar 

  29. Chua LO. (editor). Special Issue on Chaotic System, Proc. of IEEE. August 1987

    Google Scholar 

  30. Arena P, Baglio S, Fortuna L, Manganaro G. A Simplified Scheme for the Realisation of the Chua’s Oscillator by Using SC-CNN Cells. IEE Electronics Letters. 1995; 31: 1794–1795

    Article  Google Scholar 

  31. Roska T, Wu CW, Balsi M, Chua LO. Stability and Dynamics of Delay-Type General and Cellular Neural Networks. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, June 1992; 39: 6

    Article  Google Scholar 

  32. Arena P, Baglio S, Fortuna L, Manganaro G. How State Controlled CNN cells generate the dynamics of the Colpitts-like Oscillator. IEEE Trans. on Circuits and Systems — part I, July 1996; 43

    Google Scholar 

  33. Kenney MP. Chaos in the Colpitts Oscillator. IEEE Trans.on Circuits and Systems — part I, 1994; 41: 771–774

    Article  Google Scholar 

  34. Saito T. An approach toward higher dimensional hysteresis chaos generators. IEEE Trans. on Circuits and Systems 1990; 37: 399–409

    Article  MATH  Google Scholar 

  35. Suykens JAK, Vandewalle J. Generation of n-Double Scrolls (n=1,2,3,4,). IEEE Trans. on Circuits and Systems — part I, 1993; 40: 861–867

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London

About this chapter

Cite this chapter

Fortuna, L., Rizzotto, G., Lavorgna, M., Nunnari, G., Xibilia, M.G., Caponetto, R. (2001). Complex Dynamics and Cellular Neural Networks. In: Soft Computing. Advanced Textbooks in Control and Signal Processing. Springer, London. https://doi.org/10.1007/978-1-4471-0357-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0357-8_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-308-9

  • Online ISBN: 978-1-4471-0357-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics