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Gauss Chaotic Neural Networks

  • Yao-qun Xu
  • Ming Sun
  • Ji-hong Shen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4099)

Abstract

We retrospect Chen’s chaotic neural network and then propose a new chaotic neural network model whose activation function is composed of Gauss and Sigmoid function. And the time evolution figures of the largest Lyapunov exponents of chaotic single neural units are plotted. Based on the new model, the model with different parameters is applied to combinational optimization problems. 10-city traveling salesman problem (TSP) is given to make a comparison between Chen’s and the new model with different parameters. Finally on the simulation results we conclude that the novel chaotic neural network model we proposed is more effective.

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References

  1. 1.
    Hopfield, J.J., Tank, D.W.: Neural Computation of Decision in Optimization Problems. Biol. Cybern. 52, 141–152 (1985)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Hopfield, J.: Neural Networks and Physical Systems with Emergent Collective Computa-tional Abilities. Proc. Natl. Acad. Sci. 79, 2554–2558 (1982)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Hopfield, J.: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proc. Natl. Acad. Sci. 81, 3088–3092 (1984)CrossRefGoogle Scholar
  4. 4.
    Xu, Y.-Q., Sun, M., Duan, G.-R.: Wavelet Chaotic Neural Networks and Their Application to Optimization Problems. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 379–384. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Chen, L., Aihara, K.: Chaotic Simulated Annealing by a Neural Network Model with Transient Chaos. Neural Networks 8, 915–930 (1995)CrossRefGoogle Scholar
  6. 6.
    Sun, S.-Y., Zheng, J.-l.: A Kind of Improved Algorithm and Theory Testify of Solving TSP in Hopfield Neural Network. Journal of electron. 1, 73–78 (1995)Google Scholar
  7. 7.
    Potapove, A., KAli, M.: Robust Chaos in Neural Networks. Physics Letters A 277, 310–322 (2000)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Aihara, K.: Chaos engineering and its application to parallel distributed processing with chaotic neural networks. Proceedings of the IEEE 90, 919–930 (2002)CrossRefGoogle Scholar
  9. 9.
    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 Trans. System, Man, Cybern, Part B - Cybernetics 34, 2119–2125 (2004)CrossRefGoogle Scholar
  10. 10.
    Wang, L.P., Shi, H.: A noisy chaotic neural network approach to topological optimization of a communication network with reliability constraints. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3174, pp. 230–235. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Wang, L.P., Smith, K.: On chaotic simulated annealing. IEEE Trans Neural Networks 9, 716–718 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yao-qun Xu
    • 1
  • Ming Sun
    • 1
  • Ji-hong Shen
    • 2
  1. 1.Institute of Computer and Information EngineeringHarbin University of CommerceHarbinChina
  2. 2.Dept. of MathmaticsHarbin Engineering UniversityHarbinChina

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