{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T05:55:51Z","timestamp":1721368551825},"reference-count":31,"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":[[2006,9]]},"abstract":"This paper is part I of a series of contributions on the classification problem of chaos in three-dimensional autonomous quadratic systems. We try to classify chaos, based on the \u0160i'lnikov criteria, in such a large class of systems into the following four types: (1) chaos of the \u0160i'lnikov homoclinic orbit type; (2) chaos of the \u0160i'lnikov heteroclinic orbit type; (3) chaos of the hybrid type; i.e. those with both \u0160i'lnikov homoclinic and homoclinic orbits; (4) chaos of other types. We are especially interested in finding out all the simplest possible forms of chaotic systems for each type of chaos. Our main contributions are to develop some effective classification methods and to provide a basic classification framework under which each of the four types of chaos can be justified by some examples that are useful for describing the feasibility and procedure of the classification. In particular, we show several novel chaotic attractors, e.g. one hybrid-type chaotic attractor with three equilibria, one heteroclinic orbit and one homoclinic orbit, and one 4-scroll chaotic attractor with five equilibria and two heteroclinic orbits.<\/jats:p>","DOI":"10.1142\/s0218127406016203","type":"journal-article","created":{"date-parts":[[2006,11,24]],"date-time":"2006-11-24T11:27:06Z","timestamp":1164367626000},"page":"2459-2479","source":"Crossref","is-referenced-by-count":78,"title":["CLASSIFICATION OF CHAOS IN 3-D AUTONOMOUS QUADRATIC SYSTEMS-I: BASIC FRAMEWORK AND METHODS"],"prefix":"10.1142","volume":"16","author":[{"given":"TIANSHOU","family":"ZHOU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China"}]},{"given":"GUANGRONG","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. 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