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On Stability of Cellular Neural Networks

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Abstract

The main results about stability of cellular neural networks (CNNs) are reviewed. Some of them are extended and reformulated, with the purpose of providing to the CNN designer simple criteria for checking the stability properties. A particular emphasis is given to the conditions for the stability of CNNs described by space-invariant templates.

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References

  1. L.O. Chua and L. Yang, “Cellular neural networks: theory,” IEEE Transactions on Circuits and Systems, Vol. 35, No. 10, pp. 1257–1272, Oct. 1988.

    Article  MathSciNet  MATH  Google Scholar 

  2. L.O. Chua and L. Yang, “Cellular neural networks: applications,” IEEE Transactions on Circuits and Systems, Vol. 35, No. 10, pp. 1273–1290, Oct. 1988.

    Article  MathSciNet  Google Scholar 

  3. L.O. Chua and T. Roska, “The CNN paradigm,” IEEE Transactions on Circuits and Systems: I, Vol. 40, No. 3, pp. 147–156, March 1993.

    Article  MathSciNet  MATH  Google Scholar 

  4. Proceedings of the IEEE International Workshop on Cellular Neural Networks and Their Applications, Budapest, Dec. 1990.

  5. Proceedings of the Second IEEE International Workshop on Cellular Neural Networks and Their Applications, Munich, Oct. 1992.

  6. "Special issue on cellular neural networks,” International Journal of Circuit Theory and Applications, Vol. 20, No. 5, Sept.- Oct. 1992.

  7. "Special issue on cellular neural networks,” IEEE Transactions on Circuits and Systems: I-II, Vol. 40, No. 3, March 1993.

  8. Proceedings of the Third IEEE International Workshop on Cellular Neural Networks and Their Applications, Rome, Dec. 1994.

  9. "Special issue on nonlinear waves, patterns and spatio-temporal chaos in dynamic arrays,” IEEE Transactions on Circuits and Systems: I, Vol. 42, No. 10, Oct. 1995.

  10. Proceedings of the Fourth IEEE InternationalWorkshop on Cellular Neural Networks and Their Applications, Seville, June 1996.

  11. "Special issue on cellular neural networks,” International Journal of Circuit Theory and Applications, Vol. 24, No. 1-3, 1996.

  12. Proceedings of the Fifth IEEE International Workshop on Cellular Neural Networks and Their Applications, London, April 1998.

  13. F. Zou and J.A. Nossek, “Stability of cellular neural networks with opposite-sign templates,” IEEE Transactions on Circuits and Systems, Vol. 38, No. 6, pp. 675–677, June 1991.

    Article  Google Scholar 

  14. F. Zou and J.A. Nossek, “A chaotic attractor with cellular neural networks, opposite-sign templates,” IEEE Transactions on Circuits and Systems, Vol. 38, No. 7, pp. 811–812, July 1991.

    Article  Google Scholar 

  15. F. Zou and J.A. Nossek, “Bifurcation and chaos in CNN's,” IEEE Transactions on Circuits and Systems-I, Vol. 40, No. 3, pp. 166–173, March 1993.

    Article  MathSciNet  MATH  Google Scholar 

  16. P.P. Civalleri and M. Gilli, “On the dynamic behaviour of twocell cellular neural networks,” International Journal on Circuit theory and Applications, Vol. 21, pp. 451–471, 1993.

    Article  MATH  Google Scholar 

  17. P.P. Civalleri and M. Gilli, “Global dynamic behaviour of a three cell connected component detector CNN,” International Journal of Circuit Theory and Applications, Vol. 23, pp. 117–135, March-April 1995.

    Article  MATH  Google Scholar 

  18. L.O. Chua and T. Roska, “Cellular neural networks with nonlinear and delay-type template elements and non-unuform grids,” International Journal on Circuit theory and Applications, Vol. 20, pp. 449–451, 1992.

    Article  Google Scholar 

  19. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.

    Book  MATH  Google Scholar 

  20. C.W. Wu and L.O. Chua, “A more rigorous proof of complete stability of cellular neural networks,” IEEE Transactions on Circuits and Systems: I, Vol. 44, No. 4, pp. 370–371, April 1997.

    Article  MathSciNet  Google Scholar 

  21. M. Gilli, “Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions,” IEEE Transactions on Circuits and Systems-I, Vol. 41, No. 8, pp. 518–528, Aug. 1994.

    Article  MathSciNet  Google Scholar 

  22. S. Arik and V. Tavsanoglu, “Equilibrium analysis of nonsymmetric CNNs,” International Journal of Circuit Theory and Applications, Vol. 24, pp. 269–274, May-June 1996.

    Article  Google Scholar 

  23. N. Takahashi and L.O. Chua, “On the complete stability of nonsymmetric cellular neural networks,” IEEE Transactions on Circuits and Systems-I, Vol. 45, No. 7, pp. 754–758, July 1998.

    Article  MathSciNet  MATH  Google Scholar 

  24. L.O. Chua and C.W. Wu, “The universe of stable CNN templates,” International Journal of Circuit Theory and Applications: Special Issue on Cellular Neural Networks, Vol. 20, pp. 497–517, July-Aug. 1992.

    Article  MATH  Google Scholar 

  25. M.W. Hirsch, “System of differential equations that are competitive and cooperative II: convergence almost everywhere,” SIAM J. Math. Anal., Vol. 16, pp. 423–439, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  26. L.O. Chua and T. Roska, “Stability of a class of nonreciprocal cellular neural networks,” IEEE Transactions on Circuits and Systems, Vol. 37, No. 12, pp. 1520–1527, Dec. 1990.

    Article  Google Scholar 

  27. M.P. Joy and V. Tavsanoglu, “A new parameter range for the stability of opposite sign cellular neural networks,” IEEE Transactions on Circuits and Systems-I, Vol. 40, No. 3, pp. 204–207, March 1993.

    Article  MathSciNet  MATH  Google Scholar 

  28. F.A. Savaci and J. Vandewalle, “On the stability analysis of cellular neural networks,” IEEE Transactions on Circuits and Systems-I, Vol. 40, No. 3, pp. 213–215, March 1993.

    Article  MathSciNet  MATH  Google Scholar 

  29. M. Balsi, “Stability of cellular neural networks with onedimensional templates,” International Journal of Circuit Theory and Applications, Vol. 21, pp. 293–297, May-June 1993.

    Article  MATH  Google Scholar 

  30. P.P. Civalleri and M. Gilli, “Practical stability criteria for cellular neural networks,” Electronic Letters, Vol. 33, No. 11, pp. 970–971, May 1997.

    Article  Google Scholar 

  31. S. Arik and V. Tavsanoglu, “A sufficient condition for the existence of a stable equilibrium point in nonsymmetric cellular neural networks,” Proceedings of the Fifth IEEE International Workshop on Cellular Neural Networks and Their Applications, pp. 74–77, London, 1998.

  32. M.P. Joy and V. Tavsanoglu, “An equilibrium analysis of CNN's,” IEEE Transactions on Circuits and Systems-I, Vol. 45, No. 1, pp. 94–98, Jan. 1998.

    Article  MathSciNet  MATH  Google Scholar 

  33. T. Roska, C.W. Wu, M. Balsi, and L.O. Chua, “Stability and dynamics of delay-type general cellular neural networks,” IEEE Transactions on Circuits and Systems, Vol. 39, No. 6, pp. 487- 490, June 1992.

  34. T. Roska, C.W. Wu, and L.O. Chua, “Stability of CNN's with dominant nonlinear and delay-type templates,” IEEE Transactions on Circuits and Systems-I, Vol. 40, No. 4, pp. 270–272, April 1993.

    Article  MATH  Google Scholar 

  35. P.P. Civalleri, M. Gilli, and L. Pandolfi, “On stability of cellular neural networks with delay,” IEEE Transactions on Circuits and Systems-I, Vol. 40, No. 3, pp. 157–165, March 1993.

    Article  MathSciNet  Google Scholar 

  36. S. Arik and V. Tavsanoglu, “Equilibrium analysis of delayed CNNs,” IEEE Transactions on Circuits and Systems-I, Vol. 45, No. 2, pp. 168–171, 1998.

    Article  MathSciNet  Google Scholar 

  37. C. Guzelis and L.O. Chua, “Stability analysis of generalized cellular neural networks,” International Journal of Circuit Theory and Applications, Vol. 21, pp. 1–33, 1993.

    Article  MATH  Google Scholar 

  38. R. Perfetti, “Frequency domain stability criteria for cellular neural networks,” International Journal of Circuit Theory and Applications, Vol. 25, pp. 55–68, 1997.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Elettronica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129, Torino, Italy

    Pier Paolo-Civalleri & Marco Gilli

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  1. Pier Paolo-Civalleri
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  2. Marco Gilli
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Paolo-Civalleri, P., Gilli, M. On Stability of Cellular Neural Networks. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 23, 429–435 (1999). https://doi.org/10.1023/A:1008109505419

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