The local activity criteria for "difference-equation" CNN

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 2, 2001, Pages 311-419

  Sbitnev, Valery I ^b   Yang, Tao ^a   Chua, Leon O ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Russ Ac Sci ^*  (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041030593     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401002250     Document Type: Article

References (18)

1. Beck, C. & Schlögl, F. [1993] Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge).
2. Benettin, G., Galgani, L. & Strelcyn, J.-M. [1976] "Kolmogorov entropy and numerical experiments," Phys. Rev. A14(6), 2338-2345.
3. Chua, L. O. [1997] "CNN: A vision of complexity," Int. J. Bifurcation and Chaos 7(10), 2219-2425.
4. Doetsch, G. [1961] Guide to the Applications of the Laplace and Z-Transforms, Tr. ed. Fairbairn, W. M. (Van Nostrand Reinhold Co., London).
5. Dogaru, R. & Chua, L. O. [1998a] "Edge of chaos and local activity domain of FitzHugh-Nagumo equation,Int. J. Bifurcation and Chaos 8(2), 211-257.
6. Dogaru, R. & Chua, L. O. [1998b] "Edge of chaos and local activity domain of the Brusselator CNN," Int. J. Bifurcation and Chaos 8(6), 1107-1130.
7. Dogaru, R. & Chua, L. O. [1998c] "Edge of chaos and local activity domain of Gierer-Meinhardt CNN," Int. J. Bifurcation and Chaos 8(12), 1107-1130.
8. Fernándes, G. & Ortega, R. [1987] "On positive-real discrete-time transfer functions," Proc. IEEE 75(3), 428-430.
9. Ginzburg, S. L. & Sbitmev, V. I. [1999] "Spatiotemporal chaos in a 2D coupled map lattice with pinning-like force," Physica D132, 87-99.
10. Guillemin, E. A. [1957] Synthesis of Passive Networks (John Wiley, NY).
11. Hitz, L. & Anderson, B. D. O. [1969] "Discrete positive-real functions and their application to system stability," Proc. IEE 116(1), 153-155.
12. Min, L., Crounse, K. R. & Chua, L. O. [2000a] "Analytical criteria for local activity and applications to the oregonator CNN," Int. J. Bifurcation and Chaos 10(1), 25-71.
13. Min, L., Crounse, K. & Chua, L. O. [2000b] "Analytical criteria for local activity of reaction-diffusion CNN with four state variables and applications to the Hodgkin-Huxley equation," Int. J. Bifurcation and Chaos 10(6), 1295-1343.
14. Neimark, Yu. I. & Landa, P. S. [1992] Stochastic and Chaotic Oscillations (Kluwer Academic Publ., Dordrecht).
15. Sbitnev, V. I. [1998] "Chaos structure and spiral wave self-organization in 2D coupled map lattice," Int. J. Bifurcation and Chaos 8(12), 2341-2352.
16. Sbitnev, V. I. & Ampilova, N. B. [2001] "Chaotic dynamics of extracellular field potentials simulated by a neural mass network," in Biophysical Neural Networks, ed. Poznanski, R. R. (Mary Ann Liebert Inc., NY), pp. 389-409.
17. Vaidyanathan, P. P. [1985] "The discrete-time bounded-real lemma in digital filtering," IEEE Trans. Circuits Syst. CAS-32(9), 918-924.
18. Xiao, C. & Hill, D. J. [1999] "Generalization and new proof of the discrete-time positive real lemma and bounded real lemma," IEEE Trans. Circuits Syst. 46(6), 740-743.