Grazing and Chaos in a Periodically Forced, Piecewise Linear System

2004 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Linear System ◽  
Strange Attractor ◽  
Piecewise Linear ◽  
Strange Attractors ◽  
Poincaré Mapping ◽  
Grazing Bifurcation ◽  
Piecewise Linear System ◽  
Poincare Mapping

The criteria for the grazing bifurcation of a periodically forced, piecewise linear system are developed and the initial grazing manifolds are obtained. The grazing flows are illustrated. The mechanism for the fragmentation of the strange attractors caused by the grazing is discussed and the strange attractor fragmentized by grazing is illustrated through the Poincare mapping. This fragmentation phenomenon extensively exists in non-smooth dynamical systems.

Grazing and Chaos in a Periodically Forced, Piecewise Linear System

2005 ◽  
Vol 128 (1) ◽  
pp. 28-34 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Linear System ◽  
Strange Attractor ◽  
Piecewise Linear ◽  
Mathematical Structure ◽  
Strange Attractors ◽  
Grazing Bifurcation ◽  
Piecewise Linear System ◽  
Nonsmooth Dynamical Systems ◽  
Analytic Prediction

The criteria for the grazing bifurcation of a periodically forced, piecewise linear system are developed and the initial grazing manifolds are obtained. The initial grazing manifold is invariant. The grazing flows are illustrated to verify the analytic prediction of grazing. The mechanism of the strange attractors fragmentation caused by the grazing is discussed, and an illustration of the fragmentized strange attractor is given through the Poincaré mapping. This fragmentation phenomenon exists extensively in nonsmooth dynamical systems. The mathematical structure of the fragmentized strange attractors should be further developed.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
Sign in / Sign up

Export Citation Format

Share Document