Chaotic Cellular Neural Networks with Negative Self-feedback

  • Wen Liu
  • Haixiang Shi
  • Lipo Wang
  • Jacek M. Zurada
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)


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.


Chaotic Dynamic Travel Salesman Problem Chaotic Attractor Combinatorial Optimization Problem Cellular Neural Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Chua, L.O., Yang, L.: Cellular neural networks: Theory. IEEE Transactions on Circuits and Systems I 35(10), 1257–1272 (1988)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Chua, L.O., Yang, L.: Cellular neural networks: Applications. IEEE Transactions onCircuits and Systems I 35(10), 1273–1290 (1988)CrossRefMathSciNetGoogle Scholar
  3. 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)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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. 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)CrossRefMathSciNetGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    Grassi, G.: On discrete-time cellular neural networks for associative memories. IEEE Transactions on Circuits and Systems 48(1), 107–111 (2001)zbMATHCrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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. 12.
    Nozawa, H.: A neural-network model as a globally coupled map and applications based on chaos. Chaos 2(3), 377–386 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Chen, L.N., Aihara, K.: Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks 8(6), 915–930 (1995)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 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)CrossRefGoogle Scholar
  18. 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)CrossRefMathSciNetGoogle Scholar
  19. 19.
    He, Y.: Chaotic simulated annealing with decaying chaotic noise. Neural Networks, IEEE Transactions on 13(6), 1526 (2002)CrossRefGoogle Scholar
  20. 20.
    Civalleri, P.P., Gilli, M.: On stability of cellular neural networks. Journal of VLSI signal processing 23, 429–435 (1999)CrossRefGoogle Scholar
  21. 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. 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)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Gilli, M.: Strange attractors in delayed cellular neural networks. IEEE Transactions on Circuits and Systems I 40(11), 849–853 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 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. 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. 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)CrossRefGoogle Scholar
  27. 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. 28.
    Haykin, S.: Neural Networks-A comprehensive Foundation, 2nd edn. Prentice Hall International Inc., Hamilton, Canada (1999)zbMATHGoogle Scholar
  29. 29.
    Li, T., Yorke, J.: Period-3 implies chaos. Am. Math. Monthly 82, 985–992 (1975)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wen Liu
    • 1
    • 2
  • Haixiang Shi
    • 2
  • Lipo Wang
    • 1
    • 2
  • Jacek M. Zurada
    • 2
    • 3
  1. 1.College of Information EngineeringXiangtan UniversityXiangtanChina
  2. 2.School of Electrical and Electronic EngineeringNanyang Technology University, Block S1Singapore
  3. 3.Computational Intelligence Laboratory/Lutz Hall, Room 439 Electrical and Computer Engineering DepartmentUniversity of LouisvilleLouisvilleUSA

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