The Phenomenon of Delayed Bifurcation and its Analyses

2001 ◽  
pp. 203-214 ◽  
Author(s):  
Jianzhong Su
Keyword(s):  
Delayed Bifurcation

scholarly journals Delayed bifurcation in elastic snap-through instabilities

2021 ◽  
pp. 104386
Author(s):  
Mingchao Liu ◽  
Michael Gomez ◽  
Dominic Vella
Keyword(s):  
Delayed Bifurcation

A Time-Dependent Bifurcation Model with Control and Pulsing Oscillations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4260-4266
Author(s):  
Qishao Lu ◽  
Cuncai Hua
Keyword(s):  
Control Problem ◽  
Memory Effects ◽  
Time Dependent ◽  
Bifurcation Parameter ◽  
Bifurcation Transition ◽  
Delayed Bifurcation ◽  
With Memory

A time-dependent bifurcation model and its control problem are studied. Firstly, the delayed bifurcating transition with memory effects due to time-dependent parameters are analysed. Secondly, a control problem with time-dependent parametric feedback in this bifurcation model is investigated. Finally, an important mechanism for pulsing oscillation is found as the result of the delayed bifurcation transition occurring when the bifurcation parameter varies periodically across the steady bifurcation value.

DELAYED BIFURCATION IN FIRST-ORDER SINGULARLY PERTURBED PROBLEMS WITH A NONGENERIC TURNING POINT

2012 ◽  
Vol 22 (12) ◽  
pp. 1250302 ◽  
Author(s):  
JIANHE SHEN ◽  
MAOAN HAN
Keyword(s):  
Asymptotic Behavior ◽  
Hopf Bifurcation ◽  
Turning Point ◽  
Upper And Lower Solutions ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
First Order ◽  
Delayed Bifurcation ◽  
Dynamical Properties ◽  
Theoretical Results

In this paper, based on the method of upper and lower solutions, delayed bifurcation in first-order singularly perturbed problems with a nongeneric turning point is studied. The asymptotic behavior of the solutions is understood by constructing the upper and lower solutions with the desired dynamical properties. As an application of the obtained results, delayed phenomenon of degenerate Hopf bifurcation in a planar polynomial differential system with a slowly varying parameter is discussed in detail and the maximal delay is calculated. Numerical simulations are carried out to verify the theoretical results.

TIME-DEPENDENT BIFURCATION: A NEW METHOD AND APPLICATIONS

2001 ◽  
Vol 11 (12) ◽  
pp. 3153-3162 ◽  
Author(s):  
CUN-CAI HUA ◽  
QI-SHAO LU
Keyword(s):  
Qualitative Method ◽  
Time Dependent ◽  
New Method ◽  
Time Intervals ◽  
Stability Theorems ◽  
Jump Phenomena ◽  
Different Types ◽  
Bifurcation Transition ◽  
Bifurcation Problems ◽  
Delayed Bifurcation

A new qualitative method is presented for studying the bifurcation problems of nonlinear systems with time-dependent parameters. The concept of stability on finite time intervals is introduced and some related stability theorems are established in order to analyze time-dependent bifurcation problems. As some applications of the new method, three different types of delayed bifurcation transitions and jump phenomena of time-dependent Duffing–van der Pol's equation are investigated qualitatively. The bifurcation transition values are predicted by constructing the V-functions or by the linear stability. The sensitivity of motion to the initial values and parameters is also discussed.

Experimental observation of a delayed bifurcation at the threshold of an argon laser

1987 ◽  
Vol 63 (5) ◽  
pp. 344-348 ◽  
Author(s):  
W. Scharpf ◽  
M. Squicciarini ◽  
D. Bromley ◽  
C. Green ◽  
J.R. Tredicce ◽  
...  
Keyword(s):  
Experimental Observation ◽  
Argon Laser ◽  
Delayed Bifurcation

Delayed bifurcation at the threshold of a swept gain CO2 laser

1989 ◽  
Vol 70 (2) ◽  
pp. 155-160 ◽  
Author(s):  
F.T. Arecchi ◽  
W. Gadomski ◽  
R. Meucci ◽  
J.A. Roversi
Keyword(s):  
Co2 Laser ◽  
Delayed Bifurcation

scholarly journals Pattern formation in a slowly flattening spherical cap: delayed bifurcation

2020 ◽  
Vol 85 (4) ◽  
pp. 513-541
Author(s):  
Laurent Charette ◽  
Colin B Macdonald ◽  
Wayne Nagata
Keyword(s):  
Normal Form ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Centre Manifold ◽  
Spherical Cap ◽  
Centre Manifold Reduction ◽  
Delayed Bifurcation ◽  
The Stability ◽  
Parameter Values ◽  
Manifold Reduction

Abstract This article describes a reduction of a non-autonomous Brusselator reaction–diffusion system of partial differential equations on a spherical cap with time-dependent curvature using the method of centre manifold reduction. Parameter values are chosen such that the change in curvature would cross critical values which would change the stability of the patternless solution in the constant domain case. The evolving domain functions and quasi-patternless solutions are derived as well as a method to obtain this non-autonomous normal form. The coefficients of such a normal form are computed and the reduction solutions are compared to numerical solutions.

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