Double Neimark–Sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops

2006 ◽  
Vol 298 (1-2) ◽  
pp. 154-179 ◽  
Author(s):  
G.W. Luo ◽  
Y.D. Chu ◽  
Y.L. Zhang ◽  
J.G. Zhang
Keyword(s):  
Torus Bifurcation

Torus Bifurcation in Uni-Directional Coupled Gyroscopes

2009 ◽  
pp. 463-468
Author(s):  
Huy Vu ◽  
Antonio Palacios ◽  
Visarath In ◽  
Adi Bulsara ◽  
Joseph Neff ◽  
...  
Keyword(s):  
Torus Bifurcation

Torus-Bifurcation Mechanisms in a DC/DC Converter With Pulsewidth-Modulated Control

2011 ◽  
Vol 26 (4) ◽  
pp. 1270-1279 ◽  
Author(s):  
Zhanybai T. Zhusubaliyev ◽  
Erik Mosekilde ◽  
Olga O. Yanochkina
Keyword(s):  
Torus Bifurcation

Equilibrium-torus bifurcation in nonsmooth systems

2008 ◽  
Vol 237 (7) ◽  
pp. 930-936 ◽  
Author(s):  
Zhanybai T. Zhusubaliyev ◽  
Erik Mosekilde
Keyword(s):  
Nonsmooth Systems ◽  
Torus Bifurcation

scholarly journals Computational Analysis and Bifurcation of Regular and Chaotic Ca2+ Oscillations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3324
Author(s):  
Xinxin Qie ◽  
Quanbao Ji
Keyword(s):  
Numerical Simulation ◽  
Center Manifold ◽  
Computational Analysis ◽  
System Model ◽  
Phase Portraits ◽  
Bifurcation Parameter ◽  
Bifurcation Diagrams ◽  
Saddle Node Bifurcation ◽  
The Stability ◽  
Torus Bifurcation

This study investigated the stability and bifurcation of a nonlinear system model developed by Marhl et al. based on the total Ca2+ concentration among three different Ca2+ stores. In this study, qualitative theories of center manifold and bifurcation were used to analyze the stability of equilibria. The bifurcation parameter drove the system to undergo two supercritical bifurcations. It was hypothesized that the appearance and disappearance of Ca2+ oscillations are driven by them. At the same time, saddle-node bifurcation and torus bifurcation were also found in the process of exploring bifurcation. Finally, numerical simulation was carried out to determine the validity of the proposed approach by drawing bifurcation diagrams, time series, phase portraits, etc.

A POSSIBLE NEW ROUTE TO CHAOS VIA SEMICONDUCTOR SUPERLATTICES

2007 ◽  
Vol 21 (23n24) ◽  
pp. 3967-3974
Author(s):  
X. R. WANG ◽  
Z. Z. SUN ◽  
ZHENYU ZHANG
Keyword(s):  
Limit Cycles ◽  
Logistic Map ◽  
Period Doubling ◽  
Current Understanding ◽  
Semiconductor Superlattices ◽  
Frequency Locking ◽  
Routes To Chaos ◽  
Route To Chaos ◽  
Geometric Picture ◽  
Torus Bifurcation

Our current understanding of routes to chaos is mainly based on torus bifurcation where new periods are generated, the period-doubling mechanism revealed in the logistic map, and intermittency where periodic and burst motion appear alternatively. We present a possible new route to chaos based on our geometric picture of the frequency-locking of limit-cycles in semiconductor superlattices. In the period-double route and/or its variations, the period increases exponentially with bifurcation order, whereas the period in the new route increases linearly with the order of bifurcations.

scholarly journals A torus bifurcation theorem with symmetry

1990 ◽  
Vol 2 (2) ◽  
pp. 133-162 ◽  
Author(s):  
S. A. van Gils ◽  
M. Golubitsky
Keyword(s):  
Bifurcation Theorem ◽  
Torus Bifurcation
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