Results 241 to 250 of about 228,096 (272)

A Hopf bifurcation with spherical symmetry

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1992
The authors consider Hopf bifurcation on a ten dimensional center manifold in a \(O(3)\)-symmetric system. The main hypothesis is that the representation on the critical modes is given by the representation on \(V_ 5\oplus V_ 5\), the sum of two copies of the absolutely irreducible representations of \(O(3)\) on the spherical harmonics of order two ...
HAAF, H, ROBERTS, M, STEWART, I
openaire   +4 more sources

Hopf bifurcation of a fractional-order double-ring structured neural network model with multiple communication delays

Nonlinear dynamics, 2022
Shuai Li, Chengdai Huang, Sanling Yuan
semanticscholar   +1 more source

The Hopf Bifurcation

1979
Let X = Σ Xi∂i = Σ piξi∂i be a vectorfield on Δ. X is a function from Δ to RI. We define the Hessian of X at p, HPX: Tp Δ × Tp Δ → R to be the bilinear form defined by: $$ {H_P}X\left( {{Y^1}{Y^2}} \right) = {\left( {{d_P}X\left( {{Y^1}} \right),{Y^2}} \right)_P}. $$ (1.1) .
openaire   +2 more sources

Hopf Bifurcation and Time Periodic Orbits with pde2path – Algorithms and Applications

Communications in Computational Physics, 2016
We describe the algorithms used in the Matlab continuation and bifurcation package pde2path for Hopf bifurcation and continuation of branches of periodic orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the computation of Floquet ...
H. Uecker
semanticscholar   +1 more source

Reversible Equivariant Hopf Bifurcation

Archive for Rational Mechanics and Analysis, 2004
This paper is devoted to the study of codimension-one reversible Hopf bifurcation; more precisely, the authors study periodic solutions near an equilibrium whose eigenvalues collide on the imaginary axis, where such a collision arises persistently in a one-parameter family. This situation is also known as 1:1 resonance.
Buzzi, Claudio Aguinaldo, Lamb, Jeroen S. W.   +1 more
openaire   +3 more sources

The Hopf Bifurcation

An Introduction to Chaotic Dynamical Systems, 2021
R. Devaney
semanticscholar   +1 more source

THE CUSP–HOPF BIFURCATION

International Journal of Bifurcation and Chaos, 2007
The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold.
William F. Langford, John Harlim
openaire   +2 more sources

Global Hopf Bifurcation for a Predator-Prey System with Three Delays

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2017
In this paper, a delayed predator–prey model is considered. The existence and stability of the positive equilibrium are investigated by choosing the delay τ = τ1 + τ2 as a bifurcation parameter.
Zhichao Jiang, L. Wang
semanticscholar   +1 more source

Computing Hopf Bifurcations I

SIAM Journal on Numerical Analysis, 1997
Summary: This paper addresses the problems of detecting Hopf bifurcations in systems of ordinary differential equations and following curves of Hopf points in two-parameter families of vector fields. The established approach to this problem relies upon augmenting the equilibrium condition so that a Hopf bifurcation occurs at an isolated, regular point ...
John Guckenheimer, Mark Myers, Bernd Sturmfels   +2 more
openaire   +2 more sources

Hopf Bifurcation

Encyclopedia of Continuum Mechanics, 2020
Xiaojuan Sun
semanticscholar   +1 more source