{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T07:23:21Z","timestamp":1770449001863,"version":"3.49.0"},"reference-count":68,"publisher":"World Scientific Pub Co Pte Ltd","issue":"11","funder":[{"name":"National Natural Science Foundation of China (CN)","award":["11263003"],"award-info":[{"award-number":["11263003"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11533004"],"award-info":[{"award-number":["11533004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,10]]},"abstract":"<jats:p>Lyapunov exponent (LE), fast Lyapunov indicator (FLI), relative finite-time Lyapunov indicator (RLI), smaller alignment index (SALI), and generalized alignment index (GALI) are some of the available methods in most conservative systems. This study focuses on the effects of the above indicators on dissipative chaotic circuit systems such as the Lorenz system and a hyperchaotic model. Numerical experiments show that the performances of the chaos indicators in the hyperchaotic system are almost similar to those in the Lorenz system. These indicators clearly provide transition from chaotic to regular motion. However, FLI, RLI, SALI, and GALI cannot describe transition from chaos to hyperchaos. These indicators are also applied to study a new four-dimensional chaotic circuit system. The basic dynamic behaviors and structures are investigated analytically and numerically. The dynamic qualitative properties of individual orbits are observed using an oscilloscope. Moreover, the entire set of LE about the parameter is found to have three threshold values. Comparisons show that all chaos indicators are able to capture chaotic and periodic motion in chaotic circuit systems, but SALI displays significantly different behavior in several periodic orbits. SALI drops exponentially to zero for \u201cmorphologically regular\u201d orbits that are actually unstable and sensitive to perturbation. This conclusion can also be confirmed by GALI.<\/jats:p>","DOI":"10.1142\/s0218127416501820","type":"journal-article","created":{"date-parts":[[2016,10,28]],"date-time":"2016-10-28T03:08:14Z","timestamp":1477624094000},"page":"1650182","source":"Crossref","is-referenced-by-count":5,"title":["Application of Indicators for Chaos in Chaotic Circuit Systems"],"prefix":"10.1142","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3642-4668","authenticated-orcid":false,"given":"Da-Zhu","family":"Ma","sequence":"first","affiliation":[{"name":"School of Science, Hubei University for Nationalities, EnShi 445000, P. R. China"},{"name":"Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Chao","family":"Long","sequence":"additional","affiliation":[{"name":"School of Science, Hubei University for Nationalities, EnShi 445000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Science, Hubei University for Nationalities, EnShi 445000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,10,27]]},"reference":[{"key":"S0218127416501820BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(82)90171-5"},{"key":"S0218127416501820BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.14.2338"},{"key":"S0218127416501820BIB003","doi-asserted-by":"publisher","DOI":"10.1086\/159559"},{"key":"S0218127416501820BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(99)00096-4"},{"key":"S0218127416501820BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(02)00137-0"},{"key":"S0218127416501820BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-009-9194-5"},{"key":"S0218127416501820BIB007","doi-asserted-by":"publisher","DOI":"10.1086\/184976"},{"key":"S0218127416501820BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(00)00069-7"},{"key":"S0218127416501820BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001024"},{"key":"S0218127416501820BIB010","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.179001"},{"key":"S0218127416501820BIB011","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.65.533"},{"key":"S0218127416501820BIB012","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.57.617"},{"key":"S0218127416501820BIB013","unstructured":"Edward, O. [1993] Chaos in Dynamical Systems (Cambridge University Press, Cambridge), pp. 108\u2013150."},{"key":"S0218127416501820BIB014","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008276418601"},{"key":"S0218127416501820BIB015","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011141018230"},{"key":"S0218127416501820BIB016","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029343"},{"key":"S0218127416501820BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.08.005"},{"key":"S0218127416501820BIB018","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2003.1183"},{"key":"S0218127416501820BIB019","doi-asserted-by":"publisher","DOI":"10.1086\/109234"},{"key":"S0218127416501820BIB020","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/8\/6\/013"},{"key":"S0218127416501820BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412500423"},{"key":"S0218127416501820BIB022","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.89.124034"},{"key":"S0218127416501820BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s10714-014-1798-8"},{"key":"S0218127416501820BIB024","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497000509"},{"key":"S0218127416501820BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/0019-1035(90)90084-M"},{"key":"S0218127416501820BIB026","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.3515"},{"key":"S0218127416501820BIB027","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stw807"},{"key":"S0218127416501820BIB028","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"S0218127416501820BIB029","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004620"},{"key":"S0218127416501820BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740401014X"},{"key":"S0218127416501820BIB031","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411028337"},{"key":"S0218127416501820BIB032","doi-asserted-by":"publisher","DOI":"10.1016\/j.newast.2007.09.002"},{"key":"S0218127416501820BIB033","doi-asserted-by":"publisher","DOI":"10.1142\/S0129183108012996"},{"key":"S0218127416501820BIB034","doi-asserted-by":"publisher","DOI":"10.1086\/591730"},{"key":"S0218127416501820BIB035","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.89.086011"},{"key":"S0218127416501820BIB036","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-015-9628-1"},{"key":"S0218127416501820BIB037","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013276830424"},{"key":"S0218127416501820BIB038","first-page":"228","volume":"24","author":"Markov Y. G.","year":"1980","journal-title":"Soviet Astron."},{"key":"S0218127416501820BIB039","doi-asserted-by":"publisher","DOI":"10.1140\/epjc\/s10052-013-2413-y"},{"key":"S0218127416501820BIB040","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.58.125018"},{"key":"S0218127416501820BIB041","doi-asserted-by":"publisher","DOI":"10.1007\/BF00649193"},{"key":"S0218127416501820BIB042","doi-asserted-by":"publisher","DOI":"10.1109\/70.976022"},{"key":"S0218127416501820BIB043","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.1196"},{"key":"S0218127416501820BIB044","doi-asserted-by":"publisher","DOI":"10.1086\/301102"},{"key":"S0218127416501820BIB045","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2009.09.022"},{"key":"S0218127416501820BIB046","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(79)90150-6"},{"key":"S0218127416501820BIB047","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011112228708"},{"key":"S0218127416501820BIB048","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-004-8129-4"},{"key":"S0218127416501820BIB049","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.121101"},{"key":"S0218127416501820BIB050","doi-asserted-by":"publisher","DOI":"10.1515\/zna-1981-0115"},{"key":"S0218127416501820BIB051","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/47\/309"},{"key":"S0218127416501820BIB052","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/24\/006"},{"key":"S0218127416501820BIB053","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2007.04.004"},{"key":"S0218127416501820BIB054","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04458-8_2"},{"key":"S0218127416501820BIB055","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48410-4_5"},{"key":"S0218127416501820BIB056","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-007-9093-6"},{"key":"S0218127416501820BIB057","doi-asserted-by":"publisher","DOI":"10.1007\/s10569-008-9118-9"},{"key":"S0218127416501820BIB058","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(00)00033-6"},{"key":"S0218127416501820BIB059","doi-asserted-by":"crossref","first-page":"3113","DOI":"10.7498\/aps.56.3113","volume":"56","author":"Wang G. Y.","year":"2007","journal-title":"Acta Phys. Sin."},{"key":"S0218127416501820BIB060","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(03)00720-5"},{"key":"S0218127416501820BIB061","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.74.083001"},{"key":"S0218127416501820BIB062","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.76.124004"},{"key":"S0218127416501820BIB063","doi-asserted-by":"publisher","DOI":"10.1086\/516827"},{"key":"S0218127416501820BIB064","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.77.103012"},{"key":"S0218127416501820BIB065","doi-asserted-by":"publisher","DOI":"10.1016\/j.geomphys.2009.07.001"},{"key":"S0218127416501820BIB066","doi-asserted-by":"publisher","DOI":"10.1088\/1674-4527\/10\/3\/002"},{"key":"S0218127416501820BIB067","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stv1485"},{"key":"S0218127416501820BIB068","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.82.124040"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416501820","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T17:48:17Z","timestamp":1657561697000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416501820"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10]]},"references-count":68,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2016,10,27]]},"published-print":{"date-parts":[[2016,10]]}},"alternative-id":["10.1142\/S0218127416501820"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416501820","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10]]}}}