Suppression of periodic structures and the onset of hyperchaos in a parameter-space of the Baier-Sahle flow

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• 作者：Fabiola G. Prants ^{ffgrasnievicz@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Paulo C. Rech ; ^{paulo.rech@udesc.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Period-adding ; Hyperchaos ; Spiral periodic structure ; Parameter-space ; Lyapunov exponents
• 刊名：Chaos, Solitons & Fractals
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：83
• 期：Complete
• 页码：105-111
• 全文大小：1910 K

文摘

We investigate a two-dimensional parameter-space of the Baier–Sahle flow, which is a mathematical model consisting of a set of n   autonomous, four-parameter, first-order nonlinear ordinary differential equations. By using the Lyapunov exponents spectrum to numerically characterize the dynamics of the model in the chosen parameter-space, we show that for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0960077915004026&_mathId=si9.gif&_user=111111111&_pii=S0960077915004026&_rdoc=1&_issn=09600779&md5=e98a5b9e1f544bab49b0c7bd1b4f0fcc" title="Click to view the MathML source">n=3class="mathContainer hidden">class="mathCode">$n=3$ it presents typical periodic structures embedded in a chaotic region, forming a spiral structure that coils up around a focal point while period-adding bifurcations take place. We also show that these structures are destroyed as n is increased, as well as we delimit hyperchaotic regions with two or more positive Lyapunov exponents in the investigated parameter-space, for n greater than 3.