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SNAP-BACK REPELLERS AND CHAOTIC TRAVELING WAVES IN ONE-DIMENSIONAL CELLULAR NEURAL NETWORKS.
- Source :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering; Jun2007, Vol. 17 Issue 6, p1969-1983, 15p, 1 Diagram, 2 Charts, 8 Graphs
- Publication Year :
- 2007
-
Abstract
- In 1998, Chen et al. [1998] found an error in Marotto's paper [1978]. It was pointed out by them that the existence of an expanding fixed point z of a map F in B<subscript>r</subscript>(z), the ball of radius r with center at z does not necessarily imply that F is expanding in B<subscript>r</subscript>(z). Subsequent efforts (see e.g. [Chen et al., 1998; Lin et al., 2002; Li & Chen, 2003]) in fixing the problems have some discrepancies since they only give conditions for which F is expanding "locally". In this paper, we give sufficient conditions so that F is "globally" expanding. This, in turn, gives more satisfying definitions of a snap-back repeller. We then use those results to show the existence of chaotic backward traveling waves in a discrete time analogy of one-dimensional Cellular Neural Networks (CNNs). Some computer evidence of chaotic traveling waves is also given. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 17
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 26431232
- Full Text :
- https://doi.org/10.1142/S0218127407018154