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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chua, L.O., Yang, L.: Cellular neural networks: Theory. IEEE Transactions on Circuits and Systems I 35(10), 1257–1272 (1988)
Chua, L.O., Yang, L.: Cellular neural networks: Applications. IEEE Transactions onCircuits and Systems I 35(10), 1273–1290 (1988)
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)
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)
Caponetto, R., Fortuna, L., Occhipinti, L., **bilia, M.G.: Sc-cnns for chaotic signal applications in secure communication systems. International Journal of Neural Systems 13(6), 461–468 (2003)
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)
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)
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)
Grassi, G.: On discrete-time cellular neural networks for associative memories. IEEE Transactions on Circuits and Systems 48(1), 107–111 (2001)
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)
Nakaguchi, T., Omiya, K., Tanaka, M.: Hysteresis cellular neural networks for solving combinatorial optimization problems. In: Proc. of CNNA 2002, pp. 539–546 (2002)
Nozawa, H.: A neural-network model as a globally coupled map and applications based on chaos. Chaos 2(3), 377–386 (1992)
Chen, L.N., Aihara, K.: Chaotic simulated annealing by a neural network model with transient chaos. Neural Networks 8(6), 915–930 (1995)
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)
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)
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)
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)
Aihara, K.: Chaos engineering and its application to parallel distributed processing with chaotic neural networks. Proceedings of the IEEE 90(5), 919–930 (2002)
He, Y.: Chaotic simulated annealing with decaying chaotic noise. Neural Networks, IEEE Transactions on 13(6), 1526 (2002)
Civalleri, P.P., Gilli, M.: On stability of cellular neural networks. Journal of VLSI signal processing 23, 429–435 (1999)
Zou, F., Nossek, J.A.: A chaotic attractor with cellular neural networks. IEEE Transactions on Circuits and Systems I 38(7), 811–812 (1991)
Zou, F., Nossek, J.A.: Bifurcation and chaos in cellular neural networks. IEEE Transactions on Circuits and Systems I 40(3), 166–173 (1993)
Gilli, M.: Strange attractors in delayed cellular neural networks. IEEE Transactions on Circuits and Systems I 40(11), 849–853 (1993)
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)
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)
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)
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)
Haykin, S.: Neural Networks-A comprehensive Foundation, 2nd edn. Prentice Hall International Inc., Hamilton, Canada (1999)
Li, T., Yorke, J.: Period-3 implies chaos. Am. Math. Monthly 82, 985–992 (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)