Bifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps

In this work, we classify the bifurcations of chaotic attractors in 1D piecewise smooth maps from the point of view of underlying homoclinic bifurcations of repelling cycles which are located before the bifurcation at the boundary of the immediate basin of the chaotic attractor.

[1]  Soumitro Banerjee,et al.  Robust Chaos , 1998, chao-dyn/9803001.

[2]  J. Yorke,et al.  CHAOTIC ATTRACTORS IN CRISIS , 1982 .

[3]  Laura Gardini,et al.  Cyclicity of chaotic attractors in one-dimensional discontinuous maps , 2014, Math. Comput. Simul..

[4]  F. R. Marotto On redefining a snap-back repeller , 2005 .

[5]  Laura Gardini,et al.  Homoclinic bifurcations in n -dimensional endomorphisms, due to expanding periodic points , 1994 .

[6]  M. Kle Cz Ka,et al.  Local and global stability of a piecewise linear oscillator , 1992 .

[7]  Michael Schanz,et al.  On the fully developed bandcount adding scenario , 2008 .

[8]  F. R. Marotto Snap-back repellers imply chaos in Rn , 1978 .

[9]  P. De Kepper,et al.  A crisis in the Belousov-Zhabotinskii reaction: Experiment and simulation , 1987 .

[10]  Kunihiko Kaneko,et al.  Spatiotemporal chaos in one-and two-dimensional coupled map lattices , 1989 .

[11]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[12]  J. Yorke,et al.  Crises, sudden changes in chaotic attractors, and transient chaos , 1983 .

[13]  James A. Yorke,et al.  Explosions of chaotic sets , 2000 .

[14]  Laura Gardini,et al.  About Two Mechanisms of Reunion of Chaotic Attractors , 1998 .

[15]  Christian Mira,et al.  Chaotic Dynamics in Two-Dimensional Noninvertible Maps , 1996 .

[16]  Christian Mira,et al.  Some Properties of a Two-Dimensional Piecewise-Linear Noninvertible Map , 1996 .

[17]  James P. Crutchfield,et al.  Computation at the Onset of Chaos , 1991 .

[18]  James A. Yorke,et al.  Explosions: global bifurcations at heteroclinic tangencies , 2002, Ergodic Theory and Dynamical Systems.

[19]  Michael Schanz,et al.  Critical homoclinic orbits lead to snap-back repellers , 2011 .

[20]  Iryna Sushko,et al.  A Gallery of Bifurcation Scenarios in Piecewise Smooth 1D Maps , 2013 .

[21]  LAURA GARDINI,et al.  SOME CONTACT BIFURCATIONS IN TWO–DIMENSIONAL EXAMPLES , 2004 .

[22]  Laura Gardini,et al.  Degenerate bifurcations and Border Collisions in Piecewise Smooth 1D and 2D Maps , 2010, Int. J. Bifurc. Chaos.

[23]  Grebogi,et al.  Critical exponents for crisis-induced intermittency. , 1987, Physical review. A, General physics.

[24]  C. Budd,et al.  Review of ”Piecewise-Smooth Dynamical Systems: Theory and Applications by M. di Bernardo, C. Budd, A. Champneys and P. 2008” , 2020 .

[25]  Christian Mira,et al.  ON BEHAVIORS OF TWO-DIMENSIONAL ENDOMORPHISMS: ROLE OF THE CRITICAL CURVES , 1993 .