Abstract
The local activity theory introduced by Chua has provided a new tool for studying the complexity of high dimensional coupled nonlinear differential systems, in particular for reaction- diffusion cellular neural networks(R-D CNNs). In this paper some criteria for the local activity theory range from one-port to three-port cellular neural network cells with three local state variables are applied to Chen’s system. Numerical simulations show that the dynamic behaviors of the Chen’s CNN with one,two or three ports have the similar characteristics.
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Chua, L.O.: CNN: Visions of Complexity. Int. J. Bifur. and Chaos 7, 2219–2425 (1997)
Chua, L.O., Yang, L.: Cellular Neural Networks: Theory. IEEE Trans. Circuits Syst. 35, 1257–1272 (1988)
Chua, L.O., Yang, L.: Cellular Neural Networks: Applications. IEEE Trans. Circuits Syst. 35, 1273–1290 (1988)
Weblin, F., Roska, T., Chua, L.O.: The Analigic Cellular Neural Network As Bionic eye. Int. J. Circuits Theor. Appl. 23, 541–569 (1994)
Chua, L.O., Roska, T.: Cellular Neural Networks and Visual Computing. Cambridge University Press, Cambridge (2002)
Chua, L.O., Min, L.: Design for Templates with Performance of Global Connectivity Detection. Commun. Theor. Phys. 41, 151–156 (2004)
Chua, L.O.: Passivity and Complexity. IEEE Trans. Circuits Syst. I. 46, 71–82 (1999)
Dogaru, R., Chua, L.O.: Edge of Chaos and Local Activity Domain of Fitzhugh-Nagumo Equation. Int. J. Bifur. and Chaos 8, 211–257 (1998)
Dogaru, R., Chua, L.O.: Edge of Chaos and Local Activity Domain of the Brusselator CNN. Int. J. Bifur. and Chaos 8, 1107–1130 (1998)
Dogaru, R., Chua, L.O.: Edge of Chaos and Local Activity Domain of Gierer-Meinhardt CNN. Int. J. Bifur. and Chaos 8, 2321–2340 (1998)
Min, L., Crounse, K.R., Chua, L.O.: Analytical Criteria for Local Activity and Applications to the Oregonator CNN. Int. J. Bifur. and Chaos 10, 25–71 (2000)
Min, L., Crounse, K.R., Chua, L.O.: Analytical Criteria for Local Activity of Reaction-diffusion CNN with Four State Variables and Applications to the Hodgkin-Huxley Equation. Int. J. Bifur. and Chaos 8, 1295–1343 (2000)
Min, L., Yu, N.: Analytical Criteria for Local Activity of CNN with Two-port and Applications to Biochemical Model. J. Univ. Sci. Technol. Beijing 7, 305–314 (2000)
Min, L., Yu, N.: Some Analytical Criteria for Local Activity of Two-port CNN with Three or Four State Variables: Analysis and Applications. Int. J. Bifur. and Chaos 12, 931–963 (2002)
Min, L., Wang, J., Dong, X., Chen, G.: Some Analytical Criteria for Local Activity of Three-port CNN with Four State Variables: Analysis and Applications. Int. J. Bifurc.and Chaos 13, 2189–2239 (2003)
Min, L., Yu, N.: Application of Local Activity Theory of the CNN With Two Ports to the Coupled Lorenz-cell Model. Communications in Theoretical Physics 37, 759–767 (2002)
Chua, L.O.: Local Activity is the Origin of Complexity. Int. J. Bifur. and Choas 15, 3435–3456 (2005)
Huang, H., Min, L., Su, Y.: Application of Local Activity Theory to Chaotic Chemical Reaction Model. Journal of Computational and Theoretical Nnoscience 4, 1269–1273 (2007)
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Wang, D., Min, L., Ji, Y. (2008). Application of Local Activity Theory of Cellular Neural Network to the Chen’s System. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87734-9_79
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DOI: https://doi.org/10.1007/978-3-540-87734-9_79
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