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Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems\u2019 entries. Their various critical values are established and confirmed by numerical experiments demonstrating not only the loss of stability of an equilibrium point, but also other phenomena of transition to chaotic behavior. In addition, we suggest an active control method for synchronization of two chaotic fractional-order R\u00f6ssler systems. Our theoretical analysis enables to synchronize them for any value of a free parameter under which the master system displays a chaotic behavior. <\/jats:p>","DOI":"10.1142\/s0218127418500980","type":"journal-article","created":{"date-parts":[[2018,8,8]],"date-time":"2018-08-08T09:30:23Z","timestamp":1533720623000},"page":"1850098","source":"Crossref","is-referenced-by-count":18,"title":["Local Bifurcations and Chaos in the Fractional R\u00f6ssler System"],"prefix":"10.1142","volume":"28","author":[{"given":"Jan","family":"\u010cerm\u00e1k","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2, Brno 616 69, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lud\u011bk","family":"Nechv\u00e1tal","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technick\u00e1 2, Brno 616 69, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,8,8]]},"reference":[{"key":"S0218127418500980BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0263-4"},{"key":"S0218127418500980BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(00)00777-5"},{"key":"S0218127418500980BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2006.04.087"},{"key":"S0218127418500980BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.016222"},{"key":"S0218127418500980BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2009.03.010"},{"key":"S0218127418500980BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.09.064"},{"key":"S0218127418500980BIB007","first-page":"1","volume":"20","author":"Burton T. 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