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Chains in 3D Filippov systems: A chaotic phenomenon.
- Source :
-
Journal de Mathematiques Pures et Appliquees . Mar2022, Vol. 159, p168-195. 28p. - Publication Year :
- 2022
-
Abstract
- This work is devoted to the study of global connections between typical generic singularities, named T -singularities, in piecewise smooth dynamical systems. Such a singularity presents the so-called nonsmooth diabolo, which consists on a pair of invariant cones emanating from it. We analyze global features arising from the communication between the branches of a nonsmooth diabolo of a T -singularity and we prove that, under generic conditions, such communication leads to a chaotic behavior of the system. More specifically, we relate crossing orbits of a Filippov system presenting certain crossing self-connections to a T -singularity, with a Smale horseshoe of a first return map associated to the system. The techniques used in this work rely on the detection of transverse intersections between invariant manifolds of a hyperbolic fixed point of saddle type of such a first return map and the analysis of the Smale horseshoe associated to it. From the specific case discussed in our approach, we present a robust chaotic phenomenon for which its counterpart in the smooth case seems to happen only for highly degenerate systems. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CHAOS theory
*INVARIANT manifolds
*DYNAMICAL systems
*CHAOTIC communication
Subjects
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 159
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 155121105
- Full Text :
- https://doi.org/10.1016/j.matpur.2021.12.002