Canards Existence in Memristor’s Circuits

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• 作者：Jean-Marc Ginoux ; Jaume Llibre
• 关键词：Geometric singular perturbation theory ; Singularly perturbed dynamical systems ; Canard solutions
• 刊名：Qualitative Theory of Dynamical Systems
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：15
• 期：2
• 页码：383-431
• 全文大小：2,644 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Dynamical Systems and Ergodic Theory
  Difference and Functional Equations
  
• 出版者：Birkh盲user Basel
• ISSN：1662-3592
• 卷排序：15

文摘

The aim of this work is to propose an alternative method for determining the condition of existence of “canard solutions” for three and four-dimensional singularly perturbed systems with only one fast variable in the folded saddle case. This method enables to state a unique generic condition for the existence of “canard solutions” for such three and four-dimensional singularly perturbed systems which is based on the stability of folded singularities of the normalized slow dynamics deduced from a well-known property of linear algebra. This unique generic condition is perfectly identical to that provided in previous works. Application of this method to the famous three and four-dimensional memristor canonical Chua’s circuits for which the classical piecewise-linear characteristic curve has been replaced by a smooth cubic nonlinear function according to the least squares method enables to show the existence of “canard solutions” in such Memristor Based Chaotic Circuits.