{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T07:43:47Z","timestamp":1767167027320,"version":"build-2238731810"},"reference-count":11,"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 work we deal with slow\u2013fast autonomous dynamical systems. We initially define them as being modeled by systems of differential equations having a small parameter multiplying one of their velocity components. In order to analyze their solutions, some being chaotic, we have proposed a mathematical analytic method based on an iterative approach [Rossetto et al., 1998]. Under some conditions, this method allows us to give an analytic equation of the slow manifold. This equation is obtained by considering that the slow manifold is locally defined by a plane orthogonal to the tangent system's left fast eigenvector. In this paper, we give another method to compute the slow manifold equation by using the tangent system's slow eigenvectors.<\/jats:p>\n                  <jats:p>This method allows us to give a geometrical characterization of the attractor and a global qualitative description of its dynamics.<\/jats:p>\n                  <jats:p>The method used to compute the equation of the slow manifold has been extended to systems having a real and negative eigenvalue in a large domain of the phase space, as it is the case with the Lorenz system. Indeed, we give the Lorenz slow manifold equation and this allows us to make a qualitative study comparing this model and Chua's model.<\/jats:p>\n                  <jats:p>Finally, we apply our results to derive the slow manifold equations of a nonlinear optical slow\u2013fast system, namely, the optical parametric oscillator model.<\/jats:p>","DOI":"10.1142\/s0218127400001808","type":"journal-article","created":{"date-parts":[[2003,5,7]],"date-time":"2003-05-07T04:18:55Z","timestamp":1052281135000},"page":"2729-2744","source":"Crossref","is-referenced-by-count":8,"title":["SLOW MANIFOLDS OF SOME CHAOTIC SYSTEMS WITH APPLICATIONS TO LASER SYSTEMS"],"prefix":"10.1142","volume":"10","author":[{"given":"SOFIANE","family":"RAMDANI","sequence":"first","affiliation":[{"name":"University of Toulon, B.P. 132, 83957 LA GARDE Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BRUNO","family":"ROSSETTO","sequence":"additional","affiliation":[{"name":"University of Toulon, B.P. 132, 83957 LA GARDE Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LEON O.","family":"CHUA","sequence":"additional","affiliation":[{"name":"University of Toulon, B.P. 132, 83957 LA GARDE Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"REN\u00c9","family":"LOZI","sequence":"additional","affiliation":[{"name":"University of Toulon, B.P. 132, 83957 LA GARDE Cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.47.1895"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00688479"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAB.5.001063"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(75)90353-9"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02450197"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.49.2028"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496001594"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126693000290"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001765"},{"key":"p_11","author":"Suret P.","year":"1999","journal-title":"Phys. Rev. A, in press."},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749600045X"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127400001808","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:14:34Z","timestamp":1565115274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127400001808"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":11,"aliases":["10.1016\/s0218-1274(00)00180-8"],"journal-issue":{"issue":"12","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2000,12]]}},"alternative-id":["10.1142\/S0218127400001808"],"URL":"https:\/\/doi.org\/10.1142\/s0218127400001808","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}