Results 171 to 180 of about 90,042 (199)

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
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
openaire   +3 more sources

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

Stability switching at transcritical bifurcations of solitary waves in generalized nonlinear Schrödinger equations [PDF]

Physics Letters, Section A: General, Atomic and Solid State Physics, 2013
Linear stability of solitary waves near transcritical bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcation of linear-stability eigenvalues associated with this transcritical bifurcation is analytically calculated.
Jianke "Jackie" Yang
exaly   +4 more sources

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
openaire   +1 more source

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.
openaire   +1 more source

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 ...
openaire   +1 more source

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
openaire   +1 more source

A transcritical bifurcation in an immune response model

2014
[abstract]
Oliveira, Bruno, Figueiredo, I.P., Pinto, A.A., Burroughs, N.J.   +3 more
openaire   +1 more source