Results 171 to 180 of about 4,320 (200)

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 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. Muller, Steffen Waldherr, Frank Allgower   +2 more
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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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BQL Generalized Inverse Condition for Multiple Transcritical and Pitchfork Bifurcation Theorem

Numerical Functional Analysis and Optimization, 2020
In this article, by using the bounded quasi-linear projection generalized inverse, we prove the transcritical and pitchfork bifurcation theorem for multiple eigenvalues, which is a generalized resu...
Guanqi Liu, Yuwen Wang
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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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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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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
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A transcritical bifurcation in an immune response model

2014
[abstract]
Oliveira, Bruno, Figueiredo, I.P., Pinto, A.A., Burroughs, N.J.   +3 more
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Transcritical bifurcation withO(3) symmetry

Nonlinearity, 2003
Bifurcation from spherical symmetry occurs transcritically when the degree l of the spherical harmonics is even. In this case the leading-order bifurcation equations are completely determined by the symmetry. Several new results are presented concerning the existence or non-existence of solutions with dihedral symmetry in two-dimensional subspaces. For
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Invariants and stability of control systems with transcritical and saddle-node bifurcations

Proceedings of the 36th IEEE Conference on Decision and Control, 2002
State feedback control of bifurcations with quadratic or cubic degeneracy is addressed. Based on normal forms and invariants of nonlinear control systems, the classification of bifurcations for systems with a single uncontrollable mode is obtained. Using invariants, characterizations of stability are derived for a family of bifurcations, including ...
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