Bifurcations and chaos in cellular neural networks

Journal of Circuits, Systems and Computers

Volumn 12, Issue 4, 2003, Pages 417-433

  Biey, M ^a   Checco, P ^a   Gilli, M ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Bifurcation; Cellular neural networks; Chaos; Complex systems; Nonlinear circuits

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; COMPUTER SIMULATION; ELECTRIC NETWORK ANALYSIS; LARGE SCALE SYSTEMS; LYAPUNOV METHODS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION;

COMPLEX DYNAMICS; NONLINEAR CIRCUITS;

CELLULAR NEURAL NETWORKS;

EID: 0346907098     PISSN: 02181266     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218126603000957     Document Type: Article

References (29)

1. L. O. Chua and L. Yang, "Cellular neural networks: Theory", IEEE Trans. Circuits Syst. 35 (1988) 1257-1272.
2. L. O. Chua and L. Yang, "Cellular neural networks: Applications", IEEE Trans. Circuits Syst. 35 (1988) 1273-1290.
3. L. O. Chua and T. Roska, "The CNN paradigm", IEEE Trans. Circuits Syst. I 40 (1993) 147-156.
4. "Special issue on bio-inspired processors and cellular neural networks for vision", IEEE Trans. Circuits Syst. I 46, 2 (1999).
5. "Special issue on spatio-temporal signal processing with analogic CNN visual microprocessors", J. VLSI Signal Processing 23, 2/3 (1999).
6. "Special issue on cellular neural networks", Int. J. Circuit Theor. Appl. 30, 2/3 (2002) 87-393.
7. A. R. Vàzquez, M. Delgado-Restituto, E. Roca, G. Linan, R. Carmona, S. Espejo, and R. Dominguez-Castro, "CMOS analogue design primitives", Towards the Visual Microprocessor - VLSI Design and Use of Cellular Network Universal Machines, eds. T. Roska and A. Rodriguez-Vazquez, J. Wiley, Chichester, 2000, pp. 87-131.
8. M. Salerno, F. Sargeni, and V. Bonaiuto, "A dedicated multi-chip programmable system for cellular neural networks", Analog Integrated Circuits and Signal Processing 18 (1999) 277-288.
9. G. Linan, R. Dominguez-Castro, S. Espejo, and A. R. Vàzquez, "Design of a large-complexity analog I/O CNNUC", Proc. Design Automation Day on Cellular Visual Microprocessor - European Conference on Circuit Theory and Design, Stresa, Italy, Aug.-Sept. 1999, pp. 42-57.
10. P. P. Civalleri and M. Gilli, "On stability of cellular neural networks", J. VLSI Signal Processing 23 (1999) 429-435.
11. F. Zou and J. A. Nossek, "Stability of cellular neural networks with opposite-sign templates", IEEE Trans. Circuits Syst. 38 (1991) 675-677.
12. P. P. Civalleri and M. Gilli, "Global dynamic behaviour of a three-cell connected component detector CNN", Int. J. Circuit Theor. Appl. 23 (1995) 117-135.
13. N. Takahashi and T. Nishi, "On the global stability of two-cell cellular neural networks, with opposite-sign connections", Proc. European Conference on Circuit Theory and Design, Espoo, Finland, Aug. 2001, Vol. III, pp. 93-96.
14. G. Setti, P. Thiran, and C. Serpico, "An approach to information processing in one-dimensional cellular neural networks - Part II: Global propagation", IEEE Trans. Circuits Syst. I 45 (1998) 790-811.
15. P. P. Civalleri and M. Gilli, "A spectral approach to the study of propagation phenomena in CNNs", Int. J. Circuit Theor. Appl. 24 (1996) 37-47.
16. M. Gilli, "Analysis of periodic oscillations in finite-dimensional CNNs through a spatio-temporal harmonic balance technique", Int. J. Circuit Theor. Appl. 25 (1997) 279-288.
17. F. Zou and J. A. Nossek, "A chaotic attractor with cellular neural networks", IEEE Trans. Circuits Syst. I 38 (1991) 811-812.
18. P. Zou and J. A. Nossek, "Bifurcation and chaos in CNN's", IEEE Trans. Circuits Syst. I 40 (1993) 166-173.
19. M. Gilli, "Strange attractors in delayed cellular neural networks", IEEE Trans. Circuits Syst. I 40 (1993) 849-853.
20. G. Manganaro, P. Arena, and L. Fortuna, Cellular Neural Networks: Chaos, Complexity and VLSI Processing, Springer-Verlag, New York, 1999.
21. M. Biey, M. Gilli, and P. Checco, "Complex dynamic phenomena in space invariant cellular neural networks", IEEE Trans. Circuits Syst. 149 (2002) 340-344.
22. I. Petras, T. Roska, and L. O. Chua, "New spatial-temporal patterns and the first programmable on-chip bifurcation test-bed", Proc. 7th IEEE International Workshop on Cellular Neural Networks and Their Applications, Frankfurt, July 2002.
23. F. Corinto and M. Gilli, "Comparison between the dynamic behavior of Chua-Yang and full-range cellular neural networks", Internal Report, Politecnico di Torino, April 2002, submitted for publication.
24. M. Farkas, Periodic Motions, Springer-Verlag, New York, 1994, pp. 58-59.
25. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, 1989.
26. T. S. Parker and L. O. Chua, "INSITE - A software toolkit for the analysis of nonlinear dynamical systems", Proc. IEEE 75 (1987) 1081-1089.
27. H. F. Von Bremen, F. E. Udwadia, and W. Proskurowski, "An efficient QR-based method for the computation of Lyapunov exponents", Physica D 101 (1997) 1-16.
28. F. E. Udwadia, H. F. Von Bremen, and W. Proskurowski, "A note on the computation of the largest p LCEs of discrete dynamical systems", Appl. Math. Comput. 114 (2000) 205-214.
29. R. Seydel, Practical Bifurcation and Stability Analysis, Springer-Verlag, New York, 1994, Sec. 7.4.3.