{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T06:08:10Z","timestamp":1648534090156},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,6]]},"abstract":"<jats:p> 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<jats:sub>r<\/jats:sub>( z ), the ball of radius r with center at z does not necessarily imply that F is expanding in B<jats:sub>r<\/jats:sub>( z ). Subsequent efforts (see e.g. [Chen et al., 1998; Lin et al., 2002; Li &amp; 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. <\/jats:p>","DOI":"10.1142\/s0218127407018154","type":"journal-article","created":{"date-parts":[[2007,9,4]],"date-time":"2007-09-04T11:33:08Z","timestamp":1188905588000},"page":"1969-1983","source":"Crossref","is-referenced-by-count":1,"title":["SNAP-BACK REPELLERS AND CHAOTIC TRAVELING WAVES IN ONE-DIMENSIONAL CELLULAR NEURAL NETWORKS"],"prefix":"10.1142","volume":"17","author":[{"given":"YA-WEN","family":"CHANG","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R. O. 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