{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T08:10:46Z","timestamp":1767168646772,"version":"build-2238731810"},"reference-count":3,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2000,12]]},"abstract":"<jats:p>In this paper, two recursive formulas for computing the spatial entropy of two-dimensional subshifts of finite type are given. The exact entropy of a nontrivial example arising in cellular neural networks is obtained by using such formulas. We also establish some general theory concerning the spatial entropy of two-dimensional subshifts of finite type. In particular, we show that if either of the transition matrices is rank-one, then the associated exact entropy can be explicitly obtained. The generalization of our results to higher dimension can be similarly obtained. Furthermore, these formulas can be used numerically for estimating the spatial entropy.<\/jats:p>","DOI":"10.1142\/s0218127400001894","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T04:18:55Z","timestamp":1052281135000},"page":"2845-2852","source":"Crossref","is-referenced-by-count":5,"title":["THE SPATIAL ENTROPY OF TWO-DIMENSIONAL SUBSHIFTS OF FINITE TYPE"],"prefix":"10.1142","volume":"10","author":[{"given":"JONQ","family":"JUANG","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SONG-SUN","family":"LIN","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SHIH FENG","family":"SHIEH","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"WEN-WEI","family":"LIN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Tsing Hua  University, Hsinchu, Taiwan, R.O.C."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"issue":"2","key":"p_2","first-page":"108","volume":"4","author":"Chow S. N.","year":"1996","journal-title":"Rand. Comput. Dyn."},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1109\/31.7600"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139997323607"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127400001894","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:15:05Z","timestamp":1565115305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127400001894"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":3,"aliases":["10.1016\/s0218-1274(00)00189-4"],"journal-issue":{"issue":"12","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2000,12]]}},"alternative-id":["10.1142\/S0218127400001894"],"URL":"https:\/\/doi.org\/10.1142\/s0218127400001894","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}