Complex dynamics in one-dimensional CNNs

International Journal of Circuit Theory and Applications

Volumn 34, Issue 1, 2006, Pages 3-20

  Petrás, István ^a   Gilli, Marco ^b  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Cellular nonlinear networks; Chaos; Nonlinear dynamics

Indexed keywords

BOUNDARY CONDITIONS; CHAOS THEORY; DYNAMICS; PARAMETER ESTIMATION; SYSTEM STABILITY;

BIFURCATION PARAMETERS; BIFURCATION PHENOMENA; CELLULAR NONLINEAR NETWORKS;

NEURAL NETWORKS;

EID: 32344449427     PISSN: 00989886     EISSN: None     Source Type: Journal    
DOI: 10.1002/cta.340     Document Type: Article

References (29)

1. Chua LO, Yang L. Cellular neural networks: theory. IEEE Transactions on Circuits and Systems I 1988; 35: 1257-1272.
2. Wu CW, Chua LO. A more rigorous proof of complete stability of cellular neural networks. IEEE Transactions on Circuits and Systems I 1997; 44(4):370-371.
3. Chua LO, Wu CW. The universe of stable CNN templates. International Journal of Circuit Theory and Applications 1992; 20:497-517.
4. Gilli M. Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions. IEEE Transactions on Circuits and Systems I 1994; 41:518-528.
5. Takahashi N, Chua LO. On the complete stability of nonsymmetric cellular neural networks. IEEE Transactions on Circuits and Systems I 1998; 45(7):754-758.
6. Chua LO, Roska T. Stability of a class of nonreciprocal cellular neural networks. IEEE Transactions on Circuits and Systems I 1990; 37(12): 1520-1527.
7. Zou F, Nossek JA. Stability of cellular neural networks with opposite-sign templates. IEEE Transactions on Circuits and Systems I 1991; 38:675-677.
8. De Sandre G. Stability of 1-D-CNN's with Dirichlet boundary conditions and global propagation dynamics. IEEE Transactions on Circuits and Systems I 2000; 47:785-792.
9. Thiran P, Setti G, Hasler M. An approach to information propagation in 1-D cellular neural networks - Part I: local diffusion. IEEE Transactions on Circuits and Systems I 1998; 45(8):777-789.
10. Setti G, Thiran P, Hasler M. An approach to information propagation in 1-D cellular neural networks - Part II: global propagation. IEEE Transactions on Circuits and Systems I 1998; 45(8):790-811.
11. Biey M, Checco P, Gilli M. Bifurcation and chaos in CNNs. Journal of Circuits Systems and Computers 2003; 12(4):417-433.
12. Zou F, Nossek JA, Bifurcation and chaos in cellular neural networks. IEEE Transactions on Circuits and Systems I 1993; 40:166-173.
13. Biey M, Gilli M, Checco P. Complex dynamic phenomena in space-invariant cellular neural networks. IEEE Transactions on Circuits and Systems I 2002; 49(3):340-345.
14. Manganaro G, Arena P, Fortuna L. Cellular Neural Networks: Chaos, Complexity and VLSI Processing. Springer: New York, 1999 (ISBN: 3540652027).
15. Roska T, Rodríguez-Vázquez A (eds). Towards the Visual Microprocessor: VLSI Design and the Use of Cellular Network Universal Machines. Wiley: New York, 2000 (ISBN: 0471956066).
16. The ALADDIN System, http://www.analogic-computers.com/
17. Civalleri PP, Gilli M. Global dynamic behaviour of a three cell connected component detector CNN. International Journal of Circuit Theory and Applications 1995; 23(2):117-135.
18. Takahashi N, Nishi T. On the global stability of two-cell cellular neural networks with opposite-sign connections. Proceedings of the 15th European Conference on Circuit Theory and Design, vol. 3, 2001; 93-96.
19. Civalleri PP, Gilli M. A spectral approach to the study of propagation phenomena in CNNs. International Journal of Circuit Theory and Applications 1996; 24:37-48.
20. Gilli M. Analysis of periodic oscillations in finite-dimensional CNNs through a spatio-temporal harmonic balance technique. International Journal of Circuit Theory and Applications 1997; 25:279-288.
21. Di Marco M, Tesi A, Forti M. Bifurcations and oscillatory behaviour in a class of competitive cellular neural networks. International Journal of Bifurcation and Chaos 2000; 10:1267-1293.
22. Di Marco M, Forti M, Tesi A. Existence and characterization of limit cycles in nearly symmetric neural networks. IEEE Transactions on Circuits and Systems I 2002; 49(8):979-992.
23. Di Marco M, Forti M, Tesi A. Complex dynamics in nearly symmetric three-cell cellular neural networks. International Journal of Bifurcation and Chaos 2002; 12(6): 1357-1362.
24. Zou F, Nossek JA. A chaotic attractor with cellular neural networks. IEEE Transactions on Circuits and Systems I 1991; 38:811-812.
25. Gilli M. Strange attractors in delayed cellular neural networks. IEEE Transactions on Circuits and Systems I 1993; 40:849-853.
26. Petras I, Roska T, Chua LO. New spatial-temporal patterns and the first programmable on-chip bifurcation test-bed. IEEE Transactions on Circuits and Systems I 2003; 51:619-633.
27. Thiran P. Influence of boundary conditions on the behavior of cellular neural networks. IEEE Transactions on Circuits and Systems I 1993; 40:207-212.
28. Petrás I, Checco P, Gilli M, Biey M, Roska T. On the effect of boundary conditions on CNN dynamics: stability and instability; bifurcation processes and chaotic phenomena. Proceedings of ISCAS 2003, vol. III, 2003; 590-593.
29. Eckmann JP, Ruelle D. Ergodic theory of chaos and strange attractors. Reviews of Modern Physics 1985; 57: 617-659.