On global dynamic behavior of weakly connected oscillatory networks

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 4, 2005, Pages 1377-1393

  Gilli, Marco ^a   Bonnin, Michele ^a   Corinto, Fernando ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Cellular nonlinear networks; Oscillatory networks; Spectral techniques; Weakly connected networks

Indexed keywords

COMPUTER ARCHITECTURE; ELECTRICAL ENGINEERING; NEURAL NETWORKS; OSCILLATORS (ELECTRONIC); PARAMETER ESTIMATION; THEOREM PROVING;

CELLULAR NONLINEAR NETWORKS; OSCILLATORY NETWORKS; SPECTRAL TECHNIQUES; WEAKLY CONNECTED NETWORKS;

NETWORKS (CIRCUITS);

EID: 22144479071     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405012661     Document Type: Article

References (26)

1. Chua, L. O. & Yang, L. [1988a] "Cellular neural networks: Theory," IEEE Trans. Circuits Syst. 35, 1257-1272.
2. Chua, L. O. & Yang, L. [1988b] "Cellular neural networks: Applications," IEEE Trans. Circuits Syst. 35, 1273-1290.
3. Chua, L. O. & Roska, T. [1993a] "The CNN paradigm," IEEE Trans. Circuits Syst.-I 40, 147-156.
4. Chua, L. O. & Roska, T. [1993b] "The CNN universal machine: An analogic array computer," IEEE Trans. Circuits Syst.-I 40, 163-173.
5. Chua, L. O. [1995] "Special issue on nonlinear waves, patterns and spatio-temporal chaos in dynamic arrays," IEEE Trans. Circuits Syst.-I 42, 559-823.
6. Chua, L. O., Hasler, M., Moschytz, G. S. & Neirynck, J. [1995] "Autonomous cellular neural networks: A unified paradigm for pattern formation and active wave propagation," IEEE Trans. Circuits Syst.-I 42, 559-577.
7. Chua, L. O. & Roska, T. [2002] Cellular Neural Networks and Visual Computing (Cambridge University Press, UK).
8. Civalleri, P. P. & Gilli, M. [1996] "A spectral approach to the study of propagation phenomena in CNNs," Int. J. Circuit Th. Appl. 24, 37-47.
9. Crounse, K. L. & Chua, L. O. [1995] "Methods for image processing and pattern formation in cellular neural network: A tutorial," IEEE Trans. Circuits Syst.-I 42, 583-601.
10. Demmel, J. [1997] Applied Numerical Linear Algebra (SIAM, Philadelphia), p. 114.
11. Genesio, R. & Tesi, A. [1993] "Distortion control of chaotic systems: The Chua's circuit," J. Circuits Syst. Comput. 3, 151-171.
12. Gilli, M. [1995] "Investigation of chaos in large arrays of Chua's circuits via a spectral technique," IEEE Trans. Circuits Syst.-I 42, 802-806.
13. Gilli, M. [1997] "Analysis of periodic oscillations in finite-dimensional CNNs, through a spatio-temporal harmonic balance technique," Int. J. Circuit Th. Appl. 25, 279-288.
14. Gilli, M., Corinto, F. & Checco, P. [2004] "Periodicoscillations and bifurcations in cellular nonlinear networks," IEEE Trans. Circuits Syst.-I 51, 948-962.
15. Golub, G. & Van Loan, C. [1996] Matrix Computations, 3rd edition (The Johns Hopkins University Press, Baltimore), p. 198.
16. Goras, L. & Chua, L. O. [1995] "Turing patterns in CNNs: Equations and behaviors," IEEE Trans. Circuits Syst.-I 42, 612-626.
17. Hoppensteadt, F. C. & Izhikevitch, E. M. [1997] Weakly Connected Neural Networks (Springer-Verlag, NY).
18. Hoppensteadt, F. C. & Izhikevitch, E. M. [1999] "Oscillatory neurocomputers with dynamic connectivity," Phys. Rev. Lett. 82, 2983-2986.
19. Khibnik, A. I., Roose, D. & Chua, L. O. [1993] "On periodic orbits and homoclinic bifurcations in Chua's circuit with a smooth nonlinearity," J. Circuits Syst. Comput. 2, 145-178.
20. Kuramoto, Y. [1984] Chemical Oscillations, Waves and Turbulence (Springer-Verlag, NY).
21. Madan, R. N. [1993] Chua's Circuit: A Paradigm for Chaos (World Scientific, Singapore).
22. Mees, A. I. [1981] Dynamics of Feedback Systems (John Wiley, NY).
23. Osipov, G. V. & Shalfeev, V. D. [1995] "Chaos and structures in a chain of mutually-coupled Chua's circuits," IEEE Trans. Circuits Syst.-I 42, 693-699.
24. Setti, G., Thiran, P. & Serpico, C. [1998] "An approach to information processing in 1-D cellular neural networks - Part II: Global propagation," IEEE Trans. Circuits Syst.-I 45, 790-811.
25. Thiran, P., Setti, G. & Hasler, M. [1998] "An approach to information propagation in 1-D cellular neural networks - Part I: Local diffusion," IEEE Trans. Circuits Syst.-I 45, 777-789.
26. Vàzquez, A. R., Delgado-Restituto, M., Roca, E., Linan, G., Carmona, R., Espejo, S. & Dominguez-Castro, R. [2000] "CMOS analogue design primitives," in Towards the Visual Microprocessor - VLSI Design and Use of Cellular Network Universal Machines, eds. Roska, T. & Rodriguez-Vazquez, A. (J. Wiley, Chichester), pp. 87-131.