{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T10:45:06Z","timestamp":1781779506331,"version":"3.54.5"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p>In this paper, we investigate the problem of identifying or modeling nonlinear dynamical systems undergoing periodic and period-like (recurrent) motions. For accurate identification of nonlinear dynamical systems, the persistent excitation condition is normally required to be satisfied. Firstly, by using localized radial basis function networks, a relationship between the recurrent trajectories and the persistence of excitation condition is established. Secondly, for a broad class of recurrent trajectories generated from nonlinear dynamical systems, a deterministic learning approach is presented which achieves locally-accurate identification of the underlying system dynamics in a local region along the recurrent trajectory. This study reveals that even for a random-like chaotic trajectory, which is extremely sensitive to initial conditions and is long-term unpredictable, the system dynamics of a nonlinear chaotic system can still be locally-accurate identified along the chaotic trajectory in a deterministic way. Numerical experiments on the Rossler system are included to demonstrate the effectiveness of the proposed approach.<\/jats:p>","DOI":"10.1142\/s0218127409023640","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T09:02:26Z","timestamp":1250499746000},"page":"1307-1328","source":"Crossref","is-referenced-by-count":77,"title":["DETERMINISTIC LEARNING OF NONLINEAR DYNAMICAL SYSTEMS"],"prefix":"10.1142","volume":"19","author":[{"given":"CONG","family":"WANG","sequence":"first","affiliation":[{"name":"School of Automation and Center for Control and Optimization, South China University of Technology, Guangzhou 510641, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"TIANRUI","family":"CHEN","sequence":"additional","affiliation":[{"name":"School of Automation and Center for Control and Optimization, South China University of Technology, Guangzhou 510641, P. R. 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