Results 21 to 30 of about 710,736 (219)

Uniform approximations for non-generic bifurcation scenatios including bifurcations of ghost orbits [PDF]

Annals of Physics 277 (1999) 19-73, 1999
Gutzwiller's trace formula allows interpreting the density of states of a classically chaotic quantum system in terms of classical periodic orbits. It diverges when periodic orbits undergo bifurcations, and must be replaced with a uniform approximation in the vicinity of the bifurcations.
arxiv   +1 more source

Closed orbits and their bifurcations in the crossed-fields hydrogen atom [PDF]

Phys. Rev. A 67, 063410 (2003), 2002
A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for periodic orbits and allows identifying the generic closed-orbit bifurcations of codimension one.
arxiv   +1 more source

Bogdanov-Takens bifurcation of codimension $3$ in the Gierer-Meinhardt model [PDF]

arXiv, 2023
Bifurcation of the local Gierer-Meinhardt model is analyzed in this paper. It is found that the degenerate Bogdanov-Takens bifurcation of codimension 3 happens in the model, except that teh saddle-node bifurcation and the Hopf bifurcation. That was not reported in the existing results about this model.
arxiv  

Dynamical Analysis of the Lorenz-84 Atmospheric Circulation Model

Journal of Applied Mathematics, 2014
The dynamical behaviors of the Lorenz-84 atmospheric circulation model are investigated based on qualitative theory and numerical simulations. The stability and local bifurcation conditions of the Lorenz-84 atmospheric circulation model are obtained.
Hu Wang, Yongguang Yu, Guoguang Wen
doaj   +1 more source

Experiment and Theoretical Analysis Study of ETFE Inflatable Tubes

International Journal of Aerospace Engineering, 2014
The load bearing capacity of an ETFE (ethylene-tetra-fluoro-ethylene) inflatable tube is tested in this paper, and a comparative study of two wrinkling theories, the bifurcation theory and the tension field theory, is carried out for wrinkling analysis ...
YanLi He, WuJun Chen
doaj   +1 more source

Stability and Neimark–Sacker Bifurcation of a Delay Difference Equation

Mathematics, 2023
In this paper, we revisit a delay differential equation. By using the semidiscretization method, we derive its discrete model. We mainly deeply dig out a Neimark–Sacker bifurcation of the discrete model.
Shaoxia Jin, Xianyi Li
doaj   +1 more source

Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease with Time Delay

Journal of Applied Mathematics, 2014
A delay-differential modelling of vector-borne is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation theory, and its linear stability and Hopf bifurcation are demonstrated by studying the characteristic equation.
Yuanyuan Chen, Ya-Qing Bi
doaj   +1 more source

Musical tone coloring via bifurcation control of Eulerian n-tuple Hopf singularities [PDF]

Journal of Differential Equations Volume 326, 25 July 2022, Pages 129-163, 2020
An intrinsic essence of sounds in music is the evolution of their qualitative types while in mathematics we interpret each qualitative change by a bifurcation. Hopf bifurcation is an important venue to generate a signal with an arbitrary frequency. Hence, the investigations of musical sounds via bifurcation control theory are long-overdue and natural ...
arxiv   +1 more source

Introduction to bifurcation theory [PDF]

Reviews of Modern Physics, 1991
The theory of bifurcation from equilibria based on center-manifold reduction and Poincar\'e-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived.
openaire   +3 more sources

On the torus bifurcation in averaging theory [PDF]

Journal of Differential Equations, 2020
In this paper, we take advantage of the averaging theory to investigate a torus bifurcation in two-parameter families of 2D nonautonomous differential equations. Our strategy consists in looking for generic conditions on the averaged functions that ensure the existence of a curve in the parameter space characterized by a Neimark-Sacker bifurcation in ...
Douglas D. Novaes, Murilo R. Cândido
openaire   +3 more sources