Skip to main content

Chaotic Cellular Neural Networks with Negative Self-feedback

  • Conference paper
Artificial Intelligence and Soft Computing – ICAISC 2006 (ICAISC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4029))

Included in the following conference series:

Abstract

We propose a new model of Chaotic Cellular Neural Networks (C-CNNs) by introducing negative self-feedback into the Euler approximation of the continuous CNNs. According to our simulation result for the single neuron model, this new C-CNN model has richer and more flexible dynamics, compared to the conventional CNN with only stable dynamics. The hardware implementation of this new network may be important for solving a wide variety of combinatorial optimization problems.

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 139.00
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. Chua, L.O., Yang, L.: Cellular neural networks: Theory. IEEE Transactions on Circuits and Systems I 35(10), 1257–1272 (1988)

    MATH  MathSciNet  Google Scholar 

  2. Chua, L.O., Yang, L.: Cellular neural networks: Applications. IEEE Transactions onCircuits and Systems I 35(10), 1273–1290 (1988)

    Article  MathSciNet  Google Scholar 

  3. Manganaro, G., de Gyvez, J.P.: One-dimensional discrete-time cnn with multiplexed template-hardware. IEEE Transactions on Circuits and Systems I 47(5), 764–769 (2000)

    Article  Google Scholar 

  4. Bang, S.H., Sheu, B.J., Chou, E.Y.: A hardware annealing method for optimal solutions on cellular neural networks. IEEE Transactions on Circuits and Systems 43(6), 409–421 (1996)

    Article  Google Scholar 

  5. Caponetto, R., Fortuna, L., Occhipinti, L., Xibilia, M.G.: Sc-cnns for chaotic signal applications in secure communication systems. International Journal of Neural Systems 13(6), 461–468 (2003)

    Article  Google Scholar 

  6. Takahashi, N., Otake, T., Tanaka, M.: The template optimization of discrete time cnn for image compression and reconstruction. In: IEEE International Symposium on Circuits and Systems, ISCAS, pp. 237–240 (2002)

    Google Scholar 

  7. Bise, R., Takahashi, N., Nishi, T.: An improvement of the design method of cellular neural networks based on generalized eigenvalue minimization. IEEE Transactions on Circuits and Systems I 50(12), 1569–1574 (2003)

    Article  MathSciNet  Google Scholar 

  8. Wang, S., Wang, M.: A new detection algorithm (nda) based on fuzzy cellular neural networks for white blood cell detection. IEEE Transactions on information technology in biomedicine 10(1), 5–10 (2006)

    Article  Google Scholar 

  9. Grassi, G.: On discrete-time cellular neural networks for associative memories. IEEE Transactions on Circuits and Systems 48(1), 107–111 (2001)

    Article  MATH  Google Scholar 

  10. Fantacci, R., Forti, M., Pancani, L.: Cellular neural network approach to a class of communication problems. IEEE Transactions Circuits and Systems I 46(12), 1457–1467 (1999)

    Article  Google Scholar 

  11. Nakaguchi, T., Omiya, K., Tanaka, M.: Hysteresis cellular neural networks for solving combinatorial optimization problems. In: Proc. of CNNA 2002, pp. 539–546 (2002)

    Google Scholar 

  12. Nozawa, H.: A neural-network model as a globally coupled map and applications based on chaos. Chaos 2(3), 377–386 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen, L.N., Aihara, K.: Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks 8(6), 915–930 (1995)

    Article  Google Scholar 

  14. Wang, L.P., Li, S., Tian, F.Y., Fu, X.J.: A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing. IEEE Transactions on System, Man, and Cybernetics-Part B: Cybernetics 34(5), 2119–2125 (2004)

    Article  Google Scholar 

  15. He, Z., Zhang, Y., Wei, C., Wang, J.: A multistage self-organizing algorithm combined transiently chaotic neural network for cellular channel assignment. Vehicular Technology, IEEE Transactions on 51(6), 1386 (2002)

    Article  Google Scholar 

  16. Bucolo, M., Caponetto, R., Fortuna, L., Frasca, M., Rizzo, A.: Does chaos work better than noise? Circuits and Systems Magazine, IEEE 2(3), 4–19 (2002)

    Article  Google Scholar 

  17. Hayakawa, Y., Marumoto, A., Sawada, Y.: Effects of the chaotic noise on the performance of a neural network model for optimization problems. Physical review E 51(4), R2693CR2696 (1995)

    Article  Google Scholar 

  18. Aihara, K.: Chaos engineering and its application to parallel distributed processing with chaotic neural networks. Proceedings of the IEEE 90(5), 919–930 (2002)

    Article  MathSciNet  Google Scholar 

  19. He, Y.: Chaotic simulated annealing with decaying chaotic noise. Neural Networks, IEEE Transactions on 13(6), 1526 (2002)

    Article  Google Scholar 

  20. Civalleri, P.P., Gilli, M.: On stability of cellular neural networks. Journal of VLSI signal processing 23, 429–435 (1999)

    Article  Google Scholar 

  21. Zou, F., Nossek, J.A.: A chaotic attractor with cellular neural networks. IEEE Transactions on Circuits and Systems I 38(7), 811–812 (1991)

    Google Scholar 

  22. Zou, F., Nossek, J.A.: Bifurcation and chaos in cellular neural networks. IEEE Transactions on Circuits and Systems I 40(3), 166–173 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  23. Gilli, M.: Strange attractors in delayed cellular neural networks. IEEE Transactions on Circuits and Systems I 40(11), 849–853 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  24. Gilli, M., Biey, M., Civalleri, P., Checco, P.: Complex dynamics in cellular neural networks. In: Proc. of IEEE International Symposium on Circuits and Systems, pp. 45–48 (2001)

    Google Scholar 

  25. Petras, I., Checco, P., Gilli, M., Roska, T., Biey, M.: On the effect of boundary condition on cnn dynamics: Stability and instability; Bifurcation processes and chaotic phenomena. In: Proc. of ISCAS 2003, pp. 590–592 (2003)

    Google Scholar 

  26. Li, X., Ma, C., Huang, L.: Invariance principle and complete stability for cellular neural networks. IEEE Transactions on Circuits and Systems II 53(3), 202–206 (2006)

    Article  Google Scholar 

  27. Nozawa, H.: Solution of the optimization problem using the neural-network model as a globally coupled map. In: Yamaguti, M. (ed.) Towards the Harnessing of Chaos, pp. 99–114 (1994)

    Google Scholar 

  28. Haykin, S.: Neural Networks-A comprehensive Foundation, 2nd edn. Prentice Hall International Inc., Hamilton, Canada (1999)

    MATH  Google Scholar 

  29. Li, T., Yorke, J.: Period-3 implies chaos. Am. Math. Monthly 82, 985–992 (1975)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liu, W., Shi, H., Wang, L., Zurada, J.M. (2006). Chaotic Cellular Neural Networks with Negative Self-feedback. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2006. ICAISC 2006. Lecture Notes in Computer Science(), vol 4029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785231_8

Download citation

  • DOI: https://doi.org/10.1007/11785231_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35748-3

  • Online ISBN: 978-3-540-35750-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics