Equivalent CNN cell models and patterns

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 5, 2003, Pages 1055-1161

  Itoh, Makoto ^a   Chua, Leon O ^b  

^a FUKUOKA INSTITUTE OF TECHNOLOGY   (Japan)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Associative memory; Cellular neural networks; Cellular nonlinear networks; CNN; Image processing; Implicit differential equation; Pattern formation

Indexed keywords

CHAOS THEORY; DIFFERENTIAL EQUATIONS; DISCRETE TIME CONTROL SYSTEMS; GENETIC ALGORITHMS; IMAGE PROCESSING; WAVE PROPAGATION;

PATTERN FORMATION;

CELLULAR NEURAL NETWORKS;

EID: 0042198667     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127403007151     Document Type: Article

References (36)

1. Adachi, M. & Aihara, K. [1999] "An analysis on instantaneous stability of an associative chaotic neural network," Int. J. Bifurcation and Chaos 9, 2157-2163.
2. Banerjee, S., Ranjan, P. & Grebogi, C. [2000] "Bifurcation in two-dimensional piecewise smooth maps -theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I 47, 633-643.
3. Chen, L. & Aihara, K. [2000] "Strange attractors in chaotic neural networks," IEEE Trans. Circuits Syst.-I 47, 1455-1468.
4. Chua, L. O. & Lin, T. [1988] "Chaos in digital filters," IEEE Trans. Circuits Syst. 35, 648-658.
5. Chua, L. O., Yao, Y. & Yang, Q. [1990] "Generating randomness from chaos and constructing chaos with desired randomness," Int. J. Circuits Th. Appl. 18, 215-240.
6. Chua, L. O. [1993] "Global unfolding of Chua's circuit," IEICE Trans. Fundamentals E-76A, 704-734.
7. Chua, L. O. [1998] CNN: A Paradigm for Complexity (World Scientific, Singapore).
8. Chua, L. O. [1999] "Passivity and complexity," IEEE Trans. Circuits Syst.-I 46, 71-82.
9. Dogaru, R. & Chua, L. O. [1999] "Universal CNN cells," Int. J. Bifurcation and Chaos 9, 1-48.
10. Feely, O. & Chua, L. O. [1992] "Nonlinear dynamics of a class of analog-to-digital converters," Int. J. Bifurcation and Chaos 2, 325-340.
11. Hänggi, M., Moser, S., Pfaffhauser, E. & Moschytz, G. [1999] "Simulation and visualization of CNN dynamics," Int. J. Bifurcation and Chaos 9, 1237-1261.
12. Hänggi, M. & Chua, L. O. [2001] "Cellular neural networks based on resonant tunneling diodes," Int. J. Circuits Th. Appl. 29, 487-504.
13. Harrer, H. & Nossek, J. A. [1992] "Discrete-time cellular neural networks," Int. J. Circuits Th. Appl. 20, 453-467.
14. Itoh, M. [1997] "Synthesis of topologically conjugate chaotic nonlinear circuits," Int. J. Bifurcation and Chaos 7, 1195-1223.
15. Itoh, M., Wu, C. W. & Chua, L. O. [1997] "Communication systems via chaotic signals from a reconstruction viewpoint," Int. J. Bifurcation and Chaos 7, 275-286.
16. Itoh, M. [2001] "Synthesis of electronic circuits for simulating nonlinear dynamics," Int. J. Bifurcation and Chaos 11, 605-653.
17. Itoh, M., Julian, P. & Chua, L. O. [2001] "RTD-based cellular neural networks with multiple steady states," Int. J. Bifurcation and Chaos 11, 2913-2959.
18. Julian, P., Dogaru, R. & Chua, L. O. [2001] "A piecewise-linear simplicial coupling cell for CNN gray-level image processing," Proc. Int. Symp. Circuits and Systems IEEE, Sydney, Vol. III, pp. 109-112.
19. Kaneko, K. [1989] "Spatiotemporal chaos in one- and two-dimensional coupled map lattices," Physica D37, 60-82.
20. Kapral, R. [1993] "Chemical waves and coupled map lattices," in Theory and Application of Coupled Map Lattices ed. Kaneko, K. (John Wiley), pp. 135-168.
21. Lakshmanan, M. & Muruganandam, P. [2000] "Spatio-temporal patterns in arrays of coupled nonlinear electronic circuit," in Nonlinear Dynamics: Integrability and Chaos ed. Daniel, M., Tamizhmami, K. M. & Sahadevan, R. (Narosa Publishing House, New Delhi), pp. 327-343.
22. Liu, D. & Michel, A. N. [1993] "Cellular neural networks for associative memories," IEEE Trans. Circuits Syst.-II 40, 119-121.
23. Matsumoto, T., Chua, L. O. & Tanaka, S. [1984] "Simplest chaotic nonautonomous circuit," Phys. Rev. A30, 1155-1157.
24. Matsumoto, T., Chua, L. O. & Kobayashi, K. [1986] "Hyperchaos: Laboratory experiment and numerical confirmation," IEEE Trans. Circuits Syst. 33, 1143-1147.
25. Müller, B. & Reinhardt, J. [1990] Neural Networks (Springer-Verlag, NY).
26. Nozaki, H. [1992] "A neural network model as a globally coupled map and applications based on chaos," Chaos 2, 377-386.
27. Peitgen, H. O., Jürgens, H. & Saupe, D. [1992] Chaos and Fractals (Springer-Verlag, NY).
28. Pérez-Muñuzuri, A., Pérez-Muñuzuri, V., Pérez-Villar, V. & Chua, L. O. [1993] "Spiral waves on a 2-D array of nonlinear circuits," IEEE Trans. Circuits Syst.-I 40, 872-877.
29. Pikovsky, A. S. & Rabinovich, M. I. [1981] "Stochastic oscillator in dissipative systems," Physica D2, 8-24.
30. Pospíšil, J. & Kolka, Z. [2000] "Simplest ODE equivalents of Chua's equations," Int. J. Bifurcation and Chaos 10, 1-23.
31. Saito, T. [1990] "An approach toward higher dimensional hysteresis chaos generator," IEEE Trans. Circuits Syst.-I 37, 399-409.
32. Schuster, H. G. [1984] Deterministic Chaos: An Introduction (Physik-Verlag, Weinheim).
33. Shaw, S. W. & Holmes, P. J. [1983] "A periodically forced piecewise linear oscillator," J. Sound Vibr. 90, 129-155.
34. Shimura, M. [1969] Nonlinear Circuit Theory (Shoukoudo, Tokyo).
35. Wu, C. W. & Chua, L. O. [1997] "On the generality of the unfolded Chua's circuit," Int. J. Bifurcation and Chaos 6, 801-832.
36. Yang, T. & Chua, L. O. [2000] "Nonlinear dynamics of driven single-electron tunneling junctions," Int. J. Bifurcation and Chaos 10, 1091-1113.