A method for the approximate synthesis of cellular non-linear networks - Part 1: Circuit definition

International Journal of Circuit Theory and Applications

Volumn 31, Issue 3, 2003, Pages 277-297

  Storace, Marco ^a   Repetto, Lorenzo ^a   Parodi, Mauro ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

Basis functions; Cellular non linear networks; Multi terminal non linear resistors; Piecewise linear approximation

Indexed keywords

APPROXIMATION THEORY; CIRCUIT THEORY; FUNCTIONS; IMAGE PROCESSING; PARTIAL DIFFERENTIAL EQUATIONS; RESISTORS;

PIECEWISE-LINEAR (PWL) APPROACH;

CELLULAR NEURAL NETWORKS;

EID: 0038363444     PISSN: 00989886     EISSN: None     Source Type: Journal    
DOI: 10.1002/cta.232     Document Type: Article

References (20)

1. Chua LO, Hasler M, Moshytz GS, Neirynck J. Autonomous cellular neural networks: a unified paradigm for pattern formation and active wave propagation. IEEE Transactions on Circuits and Systems - I 1995; 42:559-577.
2. Corti L, De Magistris M, Maffucci A, Miano G, Serpico C, Verolino L, Visone C. Simulation of non-linear evolution equations via cellular networks. Proceedings of the European Conference on Circuit Theory and Design (ECCTD'99), Stresa, 29 August-2 September, 1999; 944-947.
3. Roska T, Chua LO, Wolf D, Kozek T, Tetzlaff R, Puffer F. Simulating non-linear waves and partial differential equations via CNN - Part I: Basic techniques. IEEE Transactions on Circuits and Systems - I 1995; 42:807-815.
4. Bonaiuto V, Maffucci A, Miano G, Salerno M, Sargeni F, Serra P, Visone C. Hardware implementation of a CNN for analog simulation of reaction-diffusion equations. Proceedings of the 2001 IEEE International Symposium on Circuits and Systems (ISCAS'2001), Sydney, 6-9 May, 2001; paper III-485.
5. Roska T, Chua LO. The CNN universal machine: an analogic array computer. IEEE Transactions on Circuits and Systems - II 1993; 40:163-173.
6. Storace M, Bizzarri F, Parodi M. Cellular non-linear networks for minimization of functionals. Part 1: Theoretical aspects. International Journal of Circuit Theory and Applications 2001; 29(2):151-167.
7. Bizzarri F, Storace M, Parodi M. Cellular non-linear networks for minimization of functionals. Part 2: Examples. International Journal of Circuit Theory and Applications 2001; 29(2):169-184.
8. Kevenaar TAM, Leenaerts D. A comparison of piecewise-linear model descriptions. IEEE Transactions on Circuits and Systems - I 1992; 39:996-1004.
9. Chua LO, Kang SM. Section-wise piecewise-linear functions: canonical representation, properties and applications. IEEE Proceedings 1977; 65:915-929.
10. Kahlert C, Chua LO. A generalized canonical piecewise-linear representation. IEEE Transactions on Circuits and Systems 1990; 37:373-383.
11. Güzeliş C, Göknar IC. A canonical representation for piecewise-affine maps and its applications to circuit analysis. IEEE Transactions on Circuits and Systems 1991; 38:1342-1354.
12. Julián P, Desages A, Agamennoni O. High-level canonical piecewise linear representation using a simplicial partition. IEEE Transactions on Circuits and Systems - I 1999; 46:463-480.
13. Van Bokhoven W. Piecewise Linear Modelling and Analysis; Kluwer, Technische Boeken: Deventer, The Netherlands, 1981.
14. Chua LO. Device modeling via basic non-linear circuit elements. IEEE Transactions on Circuits and Systems 1980; 27:1014-1044.
15. Julián P, Desages A, D'Amico B. Orthonormal high level canonical PWL functions with applications to model reduction. IEEE Transactions on Circuits and Systems - I 2000; 47:702-712.
16. Julián P, D'Amico B, Desages A. A model reduction procedure for high level canonical PWL functions. Proceedings of the 2000 IEEE International Symposium on Circuits and Systems (ISCAS'2000), Geneva, 28-31 May, 2000; paper IV-705.
17. Storace M, Julián P, Parodi M. Towards the circuit implementation of the Hodgkin-Huxley neuron model: a PWL approach. Proceedings of the 2001 IEEE International Symposium on Circuits and Systems (ISCAS'2001), Sydney, 6-9 May, 2001; paper III-823.
18. Storace M, Julián P, Parodi M. Synthesis of non-linear multi-port resistors: a PWL approach. IEEE Transactions on Circuits and Systems - I, 2002; 49(8):1138-1149.
19. Repetto L, Storace M, Parodi M. A method for the approximate synthesis of cellular non-linear networks - Part 2: Circuit reduction. International Journal of Circuit Theory and Applications, 2003; 31:299-313.
20. Floater MS, Quak EG, Reimers M. Filter bank algorithms for piecewise linear prewavelets on arbitrary triangulations. Journal of Computational and Applied Mathematics 2000; 119:185-207.