Chaos in a Piecewise Linear System with Periodic Oscillations

2013 ◽  
pp. 305-313
Author(s):  
Chunqing Lu
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Periodic Oscillations ◽  
Piecewise Linear System

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

Strange nonchaotic attractors in a periodically forced piecewise linear system with noise

Fractals ◽  
2021 ◽  
Author(s):  
Gaolei Li ◽  
Yuan Yue ◽  
Celso Grebogi ◽  
Denghui Li ◽  
Jianhua Xie
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System ◽  
Strange Nonchaotic Attractors

Multiple Harmonic Balance Method for Aperiodic Vibration of a Piecewise-Linear System

1998 ◽  
Vol 120 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Y. B. Kim
Keyword(s):  
Linear System ◽  
Harmonic Balance ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Balance Method ◽  
Piecewise Linear System ◽  
Higher Dimensional ◽  
Computational Procedures ◽  
The Stability

A multiple harmonic balance method is presented in this paper for obtaining the aperiodic steady-state solution of a piecewise-linear system. As the method utilizes general and systematic computational procedures, it can be applied to analyze the multi-tone or combination-tone responses for the higher dimensional nonlinear systems such as rotors. Moreover, it is capable of informing the stability of the obtained solution using Floquet theory. To demonstrate the systematic approach of the new method, the almost periodic forced vibration of an articulated loading platform (ALP) with a piecewise-linear stiffness is computed as an example.

ANALYTICAL SOLUTIONS OF SYSTEMS WITH PIECEWISE LINEAR DYNAMICS

2010 ◽  
Vol 20 (02) ◽  
pp. 509-518 ◽  
Author(s):  
Y. KOMINIS ◽  
T. BOUNTIS
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Piecewise Linear ◽  
Time Intervals ◽  
Linear Dynamics ◽  
Piecewise Linear System ◽  
Nonautonomous Dynamical Systems ◽  
Autonomous Component ◽  
Physical Phenomena ◽  
Linear Periodic System

A class of nonautonomous dynamical systems, consisting of an autonomous nonlinear system and an autonomous linear periodic system, each acting by itself at different time intervals, is studied. It is shown that under certain conditions for the durations of the linear and the nonlinear time intervals, the dynamics of the nonautonomous piecewise linear system is closely related to that of its nonlinear autonomous component. As a result, families of explicit periodic, nonperiodic and localized breather-like solutions are analytically obtained for a variety of interesting physical phenomena.

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