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Stability and dynamics of periodic and chaotic behaviors of the equations are investigated and the periodicity diagram is obtained in wide ranges of parameters. Regimes of both periodic and chaotic solutions are observed with complex behaviors such that the periodic regimes enclose the chaotic regime while they are also immersed inside the chaotic regime with various shapes. An asymptotic analysis is performed for sufficiently large parameters to understand the enclosure by the periodic regimes and asymptotic limit cycles are obtained to compare with limit cycles obtained from numerical results. <\/jats:p>","DOI":"10.1142\/s0218127416300159","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T02:02:54Z","timestamp":1467165774000},"page":"1630015","source":"Crossref","is-referenced-by-count":8,"title":["Periodic and Chaotic Dynamics of the Ehrhard\u2013M\u00fcller System"],"prefix":"10.1142","volume":"26","author":[{"given":"Junho","family":"Park","sequence":"first","affiliation":[{"name":"School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea"}]},{"given":"Hyunho","family":"Lee","sequence":"additional","affiliation":[{"name":"School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea"}]},{"given":"Jong-Jin","family":"Baik","sequence":"additional","affiliation":[{"name":"School of Earth and Environmental Sciences, Seoul National University, Seoul 151-742, Republic of Korea"}]}],"member":"219","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"S0218127416300159BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01009287"},{"key":"S0218127416300159BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2008.05.036"},{"key":"S0218127416300159BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.nucengdes.2014.09.011"},{"key":"S0218127416300159BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.143905"},{"key":"S0218127416300159BIB005","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/10\/5\/004"},{"key":"S0218127416300159BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740701883X"},{"key":"S0218127416300159BIB007","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112090000817"},{"key":"S0218127416300159BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.70.2714"},{"key":"S0218127416300159BIB009","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.35.927"},{"key":"S0218127416300159BIB010","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.52.2241"},{"key":"S0218127416300159BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(86)90022-9"},{"key":"S0218127416300159BIB012","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"S0218127416300159BIB013","first-page":"125","volume":"6","author":"Malkus W. 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