Stability Analysis of Periodic Orbits of Nonautonomous Piecewise-Linear Systems by Mapping Approach

2009 ◽  
Vol 56 (11) ◽  
pp. 845-849 ◽  
Author(s):  
Yibo Zhao ◽  
Jiuchao Feng ◽  
C.K. Tse
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Piecewise Linear Systems ◽  
Mapping Approach

scholarly journals Periodic orbits and invariant cones in three-dimensional piecewise linear systems

2015 ◽  
Vol 35 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Victoriano Carmona ◽  
◽  
Emilio Freire ◽  
Soledad Fernández-García ◽  
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Piecewise Linear Systems ◽  
Invariant Cones

scholarly journals Periodic orbits for perturbations of piecewise linear systems

2011 ◽  
Vol 250 (4) ◽  
pp. 2244-2266 ◽  
Author(s):  
Victoriano Carmona ◽  
Soledad Fernández-García ◽  
Emilio Freire
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Piecewise Linear Systems

Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones

1998 ◽  
Vol 08 (11) ◽  
pp. 2073-2097 ◽  
Author(s):  
Emilio Freire ◽  
Enrique Ponce ◽  
Francisco Rodrigo ◽  
Francisco Torres
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Canonical Form ◽  
Vector Fields ◽  
Piecewise Linear ◽  
Oscillatory Behavior ◽  
Linear Vector ◽  
Piecewise Linear Systems ◽  
The Creation

Planar continuous piecewise linear vector fields with two zones are considered. A canonical form which captures the most interesting oscillatory behavior is obtained and their bifurcation sets are drawn. Different mechanisms for the creation of periodic orbits are detected, and their main characteristics are emphasized.

ON PERIODIC ORBITS OF 3D SYMMETRIC PIECEWISE LINEAR SYSTEMS WITH REAL TRIPLE EIGENVALUES

2009 ◽  
Vol 19 (07) ◽  
pp. 2391-2399 ◽  
Author(s):  
E. PONCE ◽  
J. ROS
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Nonlinear Behavior ◽  
High Gain ◽  
Approximate Methods ◽  
Saturated Control ◽  
Piecewise Linear Systems

The counter-intuitive appearance of stable periodic orbits in three-dimensional piecewise linear systems has been recently reported for stable saturated control systems with high gain and real triple eigenvalues [Moreno & Suárez 2004]. In this letter using several mathematical tools, the reported sudden phenomenon is explained, and the analysis is completed by providing a global bifurcation diagram of the symmetric periodic orbits. Approximate methods are used only to illustrate the nonlinear behavior with respect to the bifurcation parameter. Analytical methods are employed to rigorously prove the main result. The employed techniques are useful not only for the family studied but also for generic three-dimensional symmetric piecewise linear systems.

scholarly journals Bifurcation Analysis of Hysteretic Systems with Saddle Dynamics

2017 ◽  
Vol 2 (2) ◽  
pp. 449-464 ◽  
Author(s):  
Marina Esteban ◽  
Enrique Ponce ◽  
Francisco Torres
Keyword(s):  
Linear Systems ◽  
Periodic Orbits ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Hysteretic Systems ◽  
Piecewise Linear Systems ◽  
Saddle Node

AbstractThis paper is devoted to the analysis of bidimensional piecewise linear systems with hysteresis coming from a reduction of symmetric 3D systems with slow-fast dynamics. We concentrate our attention on the saddle dynamics cases, determining the existence of periodic orbits as well as their stability, and possible bifurcations. Dealing with reachable saddles not in the central hysteresis band, we show the existence of subcritical/supercritical heteroclinic bifurcations as well as saddle-node bifurcations of periodic orbits.

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