{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T15:32:43Z","timestamp":1648654363561},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2004,5]]},"abstract":"<jats:p> In this paper, we apply OPCL control to discrete system, and based on relative nonlinear measure, give an algorithm for estimating the radius of stable basin. We rigorously prove that this basin is bound to be of existence for nonlinear discrete system, whose goal dynamics is either periodic orbits or fixed point. We also, in particular, investigate the stable basin in a quadratic polynomial map system, and present that the stable basin is irrelevant to the goal orbits with a negative Jacobian gain matrix. Furthermore, we take the well-known H\u00e9non system and Ikeda system as examples to illustrate the implementation of our theory, and give the corresponding simulations to reinforce our method. <\/jats:p>","DOI":"10.1142\/s0218127404010230","type":"journal-article","created":{"date-parts":[[2004,6,18]],"date-time":"2004-06-18T09:34:05Z","timestamp":1087551245000},"page":"1885-1899","source":"Crossref","is-referenced-by-count":1,"title":["ALGORITHM FOR ESTIMATION OF THE STABLE BASIN IN CONTROLLING CHAOTIC DISCRETE DYNAMICS"],"prefix":"10.1142","volume":"14","author":[{"given":"EN-GUO","family":"GU","sequence":"first","affiliation":[{"name":"Research Center and Laboratory of Mathematics  for Nonlinear Science, Department and Institute of Mathematics, Fudan University, Shanghai 200433, P. R. 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