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Hopf bifurcation formula for first order differential-delay equations
Hopf bifurcation Differential delay equation DDE Retarded functional differential equation RFDE
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2015/8/27
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The ...
Singular Hopf Bifurcation in Systems with Two Slow Variables
Hopf bifurcation mixed mode oscillation singular perturbation
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2015/8/25
Hopf bifurcations have been studied intensively in two dimensional vector fields with one slow
and one fast variable [′E. Benoˆıt et al., Collect. Math., 31 (1981), pp. 37–119; F. Dumortier...
Hopf bifurcation with zero frequency and imperfect SO(2) symmetry
Hopf bifurcation zero frequency imperfect SO(2) symmetry Dynamical Systems
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2012/6/29
Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dy...
The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
Chaos and Dynamical Systems 4D surfaces of section Hopf Bifurcation Galactic
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2011/3/2
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D
autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits
from stab...
The structure and evolution of confined tori near a Hamiltonian Hopf Bifurcation
Chaos and Dynamical Systems 4D surfaces of section Hopf Bifurcation
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2010/12/28
We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D
autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits
from stab...