Results 141 to 150 of about 890 (173)

Homoclinic flip bifurcations accompanied by transcritical bifurcation

Chinese Annals of Mathematics Series B, 2011
The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a ...
Xingbo Liu, Liu Xingbo
exaly   +3 more sources

BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION

International Journal of Bifurcation and Chaos, 2008
The bifurcations of generic heteroclinic loop with one nonhyperbolic equilibrium p1and one hyperbolic saddle p2are investigated, where p1is assumed to undergo transcritical bifurcation. Firstly, we discuss bifurcations of heteroclinic loop when transcritical bifurcation does not happen, the persistence of heteroclinic loop, the existence of homoclinic ...
Fengjie Geng, Dan Liu, Deming Zhu
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Hopf-transcritical bifurcation in retarded functional differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2010
Firstly, a codimension-two unfolding for the Hopf-transcritical bifurcation is studied, and complete bifurcation diagrams and phase portraits are given. In particular, the heteroclinic bifurcation curve is investigated explicitly, and conditions are obtained under which the secondary bifurcation periodic solutions and the heteroclinic orbit are stable.
Weihua Jiang, Hongbin Wang
exaly   +3 more sources

The transcritical bifurcation in absolutely stable feedback systems

2009 European Control Conference (ECC), 2009
The paper gives new conditions for the occurrence of a transcritical bifurcation in a non-negative passive system under non-linear static feedback. In biological systems, this provides a mechanism for defining activation thresholds in positive feedback systems.
Matthias A. Müller 0001, Steffen Waldherr, Frank Allgöwer   +2 more
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Solution and transcritical bifurcation of Burgers equation

Chinese Physics B, 2011
Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics. We can obtain many exact solutions of the Burgers equation, discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region.
Jia-Shi Tang, Ming-Hua Zhao, Feng Han, Liang Zhang   +3 more
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The saddle-node-transcritical bifurcation in a population model with constant rate harvesting

Discrete and Continuous Dynamical Systems - Series B, 2010
We study the interaction of saddle-node and transcritical bifurcations in a Lotka-Volterra model with a constant term representing harvesting or migration. Because some of the equilibria of the model lie on an invariant coordinate axis, both the saddle-node and the transcritical bifurcations are of codimension one.
Kie Van Ivanky Saputra, Lennaert Van Veen   +1 more
exaly   +3 more sources

Degenerate Transcritical Bifurcation

2014
Along two-dimensional equilibrium manifolds, we expect transcritical points, Chap. 4, to form one-dimensional curves, by the implicit-function theorem. At isolated points, one of the non-degeneracy conditions (4.8, 4.9) may fail and codimension-two singularities appear.
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Control of the saddle-node and transcritical bifurcations

IFAC Proceedings Volumes, 2004
Abstract In this paper, the control of the saddle-node and transcritical bifurcations in nonlinear systems is treated. A new approach is presented to find sufficient conditions in terms of the original vector fields. The analysis of the system dynamics is reduced to dimension one through the center manifold theorem.
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Peculiarities of equilibrium state bifurcations in transcritical mechanisms

Journal of Machinery Manufacture and Reliability, 2008
Mechanisms with one degree of freedom whose position space is characterized by self-intersection at a specified value of a coupling parameter in the field of action of a potential force are considered. Bifurcations of equilibrium positions of transcritical mechanisms and their dependence on the properties of the potential energy in the vicinity of a ...
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Bifurcation Near a Transcritical Singularity in Planar Singularly Perturbed Systems

Studies in Applied Mathematics
ABSTRACTWe classify all bifurcation phenomena of the flow near a transcritical singularity in planar singularly perturbed differential systems that do not have a breaking parameter via qualitative analysis and blow‐up technique. Here, the directional blown up vector fields can have several singularities and no first integral that are different from ...
Shen, Jianhe, Zhang, Xiang, Zhu, Kun
exaly   +2 more sources