{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T18:42:49Z","timestamp":1648579369940},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,9]]},"abstract":" We obtain numerically a horseshoe in a Poincar\u00e9 map derived from a cellular neural network described by four-dimensional autonomous ordinary differential equations. Contrary to the horseshoe numerically found in the Hodgkin\u2013Huxley model, which showed evidence that the Poincar\u00e9 map derived from the Hodgkin\u2013Huxley model has just one expanding direction on some invariant subset, the horseshoe obtained in this paper proves that the Poincar\u00e9 map derived from the neural network have two expanding directions on some invariant subset. <\/jats:p>","DOI":"10.1142\/s0218127407018968","type":"journal-article","created":{"date-parts":[[2007,11,30]],"date-time":"2007-11-30T04:59:08Z","timestamp":1196398748000},"page":"3211-3218","source":"Crossref","is-referenced-by-count":11,"title":["A HORSESHOE IN A CELLULAR NEURAL NETWORK OF FOUR-DIMENSIONAL AUTONOMOUS ORDINARY DIFFERENTIAL EQUATIONS"],"prefix":"10.1142","volume":"17","author":[{"given":"XIAO-SONG","family":"YANG","sequence":"first","affiliation":[{"name":"Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China"},{"name":"Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China"}]},{"given":"QINGDU","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511754494"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/S1111111101394040"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1995-00558-6"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-98-00945-4"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2000.3894"},{"key":"rf6","volume-title":"Dynamical Systems: Stability, Symbolic Dynamics and Chaos","author":"Robinson C.","year":"1995"},{"key":"rf7","first-page":"107","volume":"38","author":"Yan H.","journal-title":"J. Math. Chem."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404010060"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(03)00202-9"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405011631"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012818"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.04.017"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407018968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:00:29Z","timestamp":1565121629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407018968"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":12,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1142\/S0218127407018968"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407018968","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9]]}}}