On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes

Since complicated dynamical behavior can occur easily near homoclinic trajectory or heteroclinic cycle in dynamical systems with dimension not less than three, this paper investigates the existence of heteroclinic cycles in some class of 3-dimensional three-zone piecewise affine systems with two swi...

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Bibliographic Details
Published in:Nonlinear dynamics 2018, Vol.91 (1), p.67-79
Main Authors: Chen, Yanli, Wang, Lei, Yang, Xiao-Song
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Exact solutions
Manifolds (mathematics)
Mechanical Engineering
Original Paper
Planes
Switching
Vibration
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Summary:Since complicated dynamical behavior can occur easily near homoclinic trajectory or heteroclinic cycle in dynamical systems with dimension not less than three, this paper investigates the existence of heteroclinic cycles in some class of 3-dimensional three-zone piecewise affine systems with two switching planes. Based on the exact determination of the stable manifold, unstable manifold and analytic solution, a rigorous analytic methodology of designing chaos generators is proposed, which may be of potential applications to chaos secure communication. Furthermore, we obtain three sufficient conditions for the existence of a single or two heteroclinic cycles in three different cases. Finally, some examples are given to illustrate our theoretical results.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3856-8