scholarly journals Bifurcation Analysis of a Piecewise-Smooth Freeplay System

2021 ◽  
pp. 75-77
Author(s):  
Brian Evan Saunders ◽  
Rui M. G. Vasconcellos ◽  
Robert J. Kuether ◽  
Abdessattar Abdelkefi
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Smooth

scholarly journals Bifurcation analysis of piecewise smooth ecological models

2007 ◽  
Vol 72 (2) ◽  
pp. 197-213 ◽  
Author(s):  
Fabio Dercole ◽  
Alessandra Gragnani ◽  
Sergio Rinaldi
Keyword(s):  
Bifurcation Analysis ◽  
Ecological Models ◽  
Piecewise Smooth

Bifurcation analysis of an inductorless chaos generator using 1D piecewise smooth map

2014 ◽  
Vol 95 ◽  
pp. 137-145 ◽  
Author(s):  
Laura Gardini ◽  
Fabio Tramontana ◽  
Soumitro Banerjee
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Smooth ◽  
Chaos Generator ◽  
Smooth Map

scholarly journals Bifurcation Analysis of Piecewise Smooth Bimodal Maps Using Normal Form

2020 ◽  
Vol 24 (3) ◽  
pp. 137-151
Author(s):  
Z. T. Zhusubaliyev ◽  
D. S. Kuzmina ◽  
O. O. Yanochkina
Keyword(s):  
Fixed Point ◽  
Normal Form ◽  
Bifurcation Analysis ◽  
Stability Region ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Piecewise Smooth ◽  
Continuous Map ◽  
The Stability ◽  
Smooth Map

Purpose of reseach. Studyof bifurcations in piecewise-smooth bimodal maps using a piecewise-linear continuous map as a normal form. Methods. We propose a technique for determining the parameters of a normal form based on the linearization of a piecewise-smooth map in a neighborhood of a critical fixed point. Results. The stability region of a fixed point is constructed numerically and analytically on the parameter plane. It is shown that this region is limited by two bifurcation curves: the lines of the classical period-doubling bifurcation and the “border collision” bifurcation. It is proposed a method for determining the parameters of a normal form as a function of the parameters of a piecewise smooth map. The analysis of "border-collision" bifurcations using piecewise-linear normal form is carried out. Conclusion. A bifurcation analysis of a piecewise-smooth irreversible bimodal map of the class Z1–Z3–Z1 modeling the dynamics of a pulse–modulated control system is carried out. It is proposed a technique for calculating the parameters of a piecewise linear continuous map used as a normal form. The main bifurcation transitions are calculated when leaving the stability region, both using the initial map and a piecewise linear normal form. The topological equivalence of these maps is numerically proved, indicating the reliability of the results of calculating the parameters of the normal form.

Bifurcation analysis of a piecewise smooth system with non-linear characteristics

2005 ◽  
Vol 33 (4) ◽  
pp. 263-279 ◽  
Author(s):  
Takuji Kousaka ◽  
Tetsushi Ueta ◽  
Yue Ma ◽  
Hiroshi Kawakami
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Smooth ◽  
Piecewise Smooth System ◽  
Non Linear ◽  
Smooth System

Bifurcation Analysis of Planar Piecewise Smooth Systems with a Line of Discontinuity

2016 ◽  
Vol 26 (06) ◽  
pp. 1650104
Author(s):  
Dingheng Pi ◽  
Shihong Xu
Keyword(s):  
Hamiltonian System ◽  
Linear System ◽  
Qualitative Analysis ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Piecewise Smooth ◽  
Piecewise Smooth Systems ◽  
Differential Systems ◽  
Line Of Discontinuity ◽  
Smooth System

In this paper, we consider bifurcations of a class of planar piecewise smooth differential systems constituted by a general linear system and a quadratic Hamiltonian system. The linear system has four parameters. When the parameters vary in different regions, the left linear system can have a saddle, a node or a focus. For each case, we provide a completely qualitative analysis of the dynamical behavior for this piecewise smooth system. Our results generalize and improve the results in this direction.

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