Chaotic behavior analysis based on sliding bifurcations

In this paper, a mathematical analysis of a possible way to chaos for bounded piecewise smooth systems of dimension 3 submitted to one of it's specific bifurcations, namely the sliding ones, is proposed. This study is based on period doubling method applied to the relied Poincare maps.

[1]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[2]  Driss Boutat,et al.  New Type of Data Transmission Using a Synchronization of Chaotic Systems , 2005, Int. J. Bifurc. Chaos.

[3]  Kannan M. Moudgalya,et al.  A class of discontinuous dynamical systems II. An industrial slurry high density polyethylene reactor , 2001 .

[4]  D. Benmerzouk,et al.  Lyapunov-Schmidt method dedicated to the observer analysis and design , 2006 .

[5]  S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[6]  Jean-Pierre Barbot,et al.  Chaotic behavior analysis based on corner bifurcations , 2009 .

[7]  M. I. Feigin,et al.  On the structure of C-bifurcation boundaries of piecewise-continuous systems , 1978 .

[8]  P. Glendinning Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations , 1994 .

[9]  M. di Bernardo,et al.  Bifurcations of dynamical systems with sliding: derivation of normal-form mappings , 2002 .

[10]  C J Budd,et al.  Grazing and border-collision in piecewise-smooth systems: a unified analytical framework. , 2001, Physical review letters.

[11]  Alan R. Champneys,et al.  Unified Framework for the analysis of grazing and border-collisions in piecewise-smooth systems , 2001 .

[12]  Jean-Pierre Barbot,et al.  Grazing Analysis for Synchronization of chaotic hybrid systems , 2007 .

[13]  J. Barbot,et al.  Observability analysis using Lyapunov-Schmidt method , 2004 .

[14]  Mario di Bernardo,et al.  Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter , 1998 .

[15]  James A. Yorke,et al.  BORDER-COLLISION BIFURCATIONS FOR PIECEWISE SMOOTH ONE-DIMENSIONAL MAPS , 1995 .

[16]  Alan R. Champneys,et al.  Normal form maps for grazing bifurcations in n -dimensional piecewise-smooth dynamical systems , 2001 .

[17]  Shouchuan Hu Differential equations with discontinuous right-hand sides☆ , 1991 .