Tangent bifurcation in doubling period process of a resonant circuit's responses

2005 ◽  
Author(s):  
H. Khammari ◽  
M. Benrejeb
Keyword(s):  
Tangent Bifurcation

scholarly journals Investigation of the Mechanism of Tangent Bifurcation in Current Mode Controlled Boost Converter

2011 ◽  
Vol 02 (01) ◽  
pp. 38-44 ◽  
Author(s):  
Ling-ling Xie ◽  
Ren-xi Gong ◽  
Kuang Wang ◽  
Hao-ze Zhuo
Keyword(s):  
Current Mode ◽  
Boost Converter ◽  
Tangent Bifurcation

scholarly journals Investigation of tangent bifurcation in voltage mode controlled DCM boost converters

2012 ◽  
Vol 61 (5) ◽  
pp. 058401
Author(s):  
Xie Ling-Ling ◽  
Gong Ren-Xi ◽  
Zhuo Hao-Ze ◽  
Ma Xian-Hua
Keyword(s):  
Boost Converters ◽  
Voltage Mode ◽  
Tangent Bifurcation

SUNSPOT ACTIVITY CURVES AND INTERMITTENT CHAOTIC BEHAVIOR

1995 ◽  
Vol 05 (04) ◽  
pp. 1213-1219
Author(s):  
GÜLŞEN GÜRBÜZ ◽  
CHRISTIAN BECK
Keyword(s):  
Chaotic Behavior ◽  
Logistic Map ◽  
Maunder Minimum ◽  
Sunspot Activity ◽  
Characteristic Numbers ◽  
Injection Model ◽  
Tangent Bifurcation ◽  
Low Dimensional ◽  
Grand Minima

We analyze the statistical properties of observed sunspot numbers. Near the Maunder minimum, the dynamics of successive sunspot maxima is low-dimensional and has properties similar to the intermittent logistic map. The long-term statistics is well described by an intermittent random injection model with Poissonian injection statistics. Three different characteristic numbers are extracted from the solar signal: The distance from the critical point of tangent bifurcation, the injection probability into the laminar phase, and the relaxation time of correlations. It is suggested to interpret the grand minima of the solar cycle as the laminar phase of the intermittent solar dynamo.

scholarly journals Phase Multistability of Dynamics Modes of the Ricker Model with Periodic Malthusian Parameter

2018 ◽  
Vol 13 (1) ◽  
pp. 68-83
Author(s):  
K.V. Shlufman ◽  
G.P. Neverova ◽  
E.Ya. Frisman
Keyword(s):  
Phase Shift ◽  
Dynamic Mode ◽  
Threshold Values ◽  
Attraction Basin ◽  
Malthusian Parameter ◽  
Ricker Model ◽  
Short Period ◽  
Tangent Bifurcation ◽  
Attraction Basins ◽  
Model Trajectory

The paper investigates the phase multistability of dynamical modes of the Ricker model with 2-year periodic Malthusian parameter. It is shown that both the variable perturbation and the phase shift of the Malthusian parameter can lead to a phase shift or a change in the dynamic mode observed. The possibility of switches between different dynamic modes is due to multistability, since the model has two different stable 2-cycles. The first stable 2-cycle is the result of transcritical bifurcation and is synchronous to the oscillations of the Malthusian parameter. The second stable 2-cycle arises as a result of the tangent bifurcation and is asynchronous to the oscillations of the Malthusian parameter. This indicates that two-year fluctuations in the population size can be both synchronous and asynchronous to the fluctuations in the environment. The phase shift of the Malthusian parameter causes a phase shift in the stable 4-cycle of the first bifurcation series to one or even three elements of the 4-cycle. The phase shift to two elements of this 4-cycle is possible due to a change in the half-amplitude of the Malthusian parameter oscillation or the variable perturbation. At the same time, the longer period of the cycle, the more phases with their attraction basins it has, and the smaller the threshold values above which shift from the attraction basin to another one occur. As a result, in the case of cycles with long period (for example, 8-cycle) perturbations, that stable cycles with short period are able to "absorb", can cause different phase transitions, which significantly complicates the dynamics of the model trajectory and, as a consequence, the identification of the dynamic mode observed.

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