On the Templates Corresponding to Cycle-Symmetric Connectivity in Cellular Neural Networks

In the architecture of cellular neural networks (CNN), connections among cells are built on linear coupling laws. These laws are characterized by the so-called templates which express the local interaction weights among cells. Recently, the complete stability for CNN has been extended from symmetric connections to cycle-symmetric connections. In this presentation, we investigate a class of two-dimensional space-invariant templates. We find necessary and sufficient conditions for the class of templates to have cycle-symmetric connections. Complete stability for CNN with several interesting templates is thus concluded.

[1]  Tom,et al.  Structure and Dynamics of Artiicial Neural Networks , 2022 .

[2]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[3]  Shui-Nee Chow,et al.  DYNAMICS OF LATTICE DIFFERENTIAL EQUATIONS , 1996 .

[4]  Shyan-Shiou Chen,et al.  Dynamics for Discrete-Time Cellular Neural Networks , 2004, Int. J. Bifurc. Chaos.

[5]  L.O. Chua,et al.  Cellular neural networks , 1993, 1988., IEEE International Symposium on Circuits and Systems.

[6]  John Mallet-Paret,et al.  Pattern Formation and Spatial Chaos in Spatially Discrete Evolution Equations , 1995 .

[7]  Leon O. Chua,et al.  On the universe of stable cellular neural networks , 1992, Int. J. Circuit Theory Appl..

[8]  Chih-Wen Shih,et al.  Exact Number of Mosaic Patterns in Cellular Neural Networks , 2001, Int. J. Bifurc. Chaos.

[9]  L. Chua.  Cnn: A Paradigm for Complexity , 1998 .

[10]  W. M. Oliva,et al.  An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory , 1983 .

[11]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[12]  P. Thiran,et al.  Influence of boundary conditions on the behavior of cellular neural networks , 1993 .

[13]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[14]  B. Fiedler,et al.  A class of convergent neural network dynamics , 1998 .

[15]  Jack K. Hale,et al.  Convergence in gradient-like systems with applications to PDE , 1992 .

[16]  Chih-Wen Shih,et al.  Cycle-symmetric matrices and convergent neural networks , 2000 .

[17]  Chih-Wen Shih,et al.  Pattern Formation and Spatial Chaos for Cellular Neural Networks with Asymmetric Templates , 1998 .

[18]  Chih-Wen Shih.  Influence of Boundary Conditions on Pattern Formation and Spatial Chaos in Lattice Systems , 2000, SIAM J. Appl. Math..

[19]  M. Hirsch.  Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere , 1985 .

[20]  Chih-Wen Shih,et al.  Complete Stability for Standard Cellular Neural Networks , 1999 .

[21]  Shui-Nee Chow,et al.  Pattern formation and spatial chaos in lattice dynamical systems. II , 1995 .

[22]  Marco Gilli,et al.  Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions , 1994 .

[23]  L. Chua,et al.  A more rigorous proof of complete stability of cellular neural networks , 1997 .

[24]  Jonq Juang,et al.  Cellular Neural Networks: Mosaic Pattern and Spatial Chaos , 2000, SIAM J. Appl. Math..

[25]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[26]  Chih-Wen Shih,et al.  Complete stability for a Class of Cellular Neural Networks , 2001, Int. J. Bifurc. Chaos.

[27]  Jonq Juang,et al.  Cellular Neural Networks: Pattern Formation and Spatial Chaos , 1999 .