16,763 research outputs found
Controlling Delay-induced Hopf bifurcation in Internet congestion control system
This paper focuses on Hopf bifurcation control in a dual model of Internet
congestion control algorithms which is modeled as a delay differential equation
(DDE). By choosing communication delay as a bifurcation parameter, it has been
demonstrated that the system loses stability and a Hopf bifurcation occurs when
communication delay passes through a critical value. Therefore, a time-delayed
feedback control method is applied to the system for delaying the onset of
undesirable Hopf bifurcation. Theoretical analysis and numerical simulations
confirm that the delayed feedback controller is efficient in controlling Hopf
bifurcation in Internet congestion control system. Moreover, the direction of
the Hopf bifurcation and the stability of the bifurcating periodic solutions
are determinated by applying the center manifold theorem and the normal form
theory.Comment: 20 pages, 8 figure
Nonstandard Hopf bifurcation in switched
This paper presents an analysis on nonstandard generalized Hopf bifurcation
in a class of switched systems where the lost of stability of linearized
systems is not due to the crossing of their complex conjugate eigenvalues but
relevant to the switching laws between the subslystems. Thus is remarkably
different from the mechanism of the Hopf bifurcation and the generalized Hopf
bifurcation studied in the literature.Comment: 15 pages, 5 figure
Hopf-type neurons increase input-sensitivity by forming forcing-coupled ensembles
Astounding properties of biological sensors can often be mapped onto a
dynamical system in the vicinity a bifurcation. For mammalian hearing, a Hopf
bifurcation description has been shown to work across a whole range of scales,
from individual hair bundles to whole regions of the cochlea. We reveal here
the origin of this scale-invariance, from a general level, applicable to all
neuronal dynamics in the vicinity of a Hopf bifurcation (embracing, e.g.,
Hodgkin-Huxley equations). When coupled by natural 'force-coupling', ensembles
of Hopf oscillators below bifurcation threshold exhibit a collective Hopf
bifurcation. This collective Hopf bifurcation occurs substantially below where
the average of the individual oscillators would bifurcate, with a frequency
profile that is sharpened if compared to the individual oscillators
Two delays induce Hopf bifurcation and double Hopf bifurcation in a diffusive Leslie-Gower predator-prey system
In this paper, the dynamics of a modified Leslie-Gower predator-prey system
with two delays and diffusion is considered. By calculating stability switching
curves, the stability of positive equilibrium and the existence of Hopf
bifurcation and double Hopf bifurcation are investigated on the parametric
plane of two delays. Taking two time delays as bifurcation parameters, the
normal form on the center manifold near the double Hopf bifurcation point is
derived, and the unfoldings near the critical points are given. Finally, we
obtain the complex dynamics near the double Hopf bifurcation point, including
the existence of quasi-periodic solutions on a 2-torus, quasi-periodic
solutions on a 3-torus, and strange attractors
Hopf bifurcation for a delayed diffusive logistic population model in the advective heterogeneous environment
In this paper, we investigate a delayed reaction-diffusion-advection
equation, which models the population dynamics in the advective heterogeneous
environment. The existence of the nonconstant positive steady state and
associated Hopf bifurcation are obtained. A weighted inner product associated
with the advection rate is introduced to compute the normal forms, which is the
main difference between Hopf bifurcation for delayed
reaction-diffusion-advection model and that for delayed reaction-diffusion
model. Moreover, we find that the spatial scale and advection can affect Hopf
bifurcation in the heterogenous environment.Comment: 30 page
Hopf points of codimension two in a delay differential equation modeling leukemia
This paper continues the work contained in two previous papers, devoted to
the study of the dynamical system generated by a delay differential equation
that models leukemia. Here our aim is to identify degenerate Hopf bifurcation
points. By using an approximation of the center manifold, we compute the first
Lyapunov coefficient for Hopf bifurcation points. We find by direct
computation, in some zones of the parameter space (of biological significance),
points where the first Lyapunov coefficient equals zero. For these we compute
the second Lyapunov coefficient, that determines the type of the degenerate
Hopf bifurcation
Hopf Bifurcations in Replicator Dynamics with Distributed Delays
In this paper, we study the existence and the property of the Hopf
bifurcation in the two-strategy replicator dynamics with distributed delays. In
evolutionary games, we assume that a strategy would take an uncertain time
delay to have a consequence on the fitness (or utility) of the players. As the
mean delay increases, a change in the stability of the equilibrium (Hopf
bifurcation) may occur at which a periodic oscillation appears. We consider
Dirac, uniform, Gamma, and discrete delay distributions, and we use the
Poincar\'e- Lindstedt's perturbation method to analyze the Hopf bifurcation.
Our theoretical results are corroborated with numerical simulations
The stability and Hopf bifurcation of the diffusive Nicholson's blowflies model in spatially heterogeneous environment
In this paper, we consider the diffusive Nicholson's blowflies model in
spatially heterogeneous environment when the diffusion rate is large. We show
that the ratio of the average of the maximum per capita egg production rate to
that of the death rate affects the dynamics of the model. The unique positive
steady state is locally asymptotically stable if the ratio is less than a
critical value. However, when the ratio is greater than the critical value,
large time delay can make the unique positive steady state unstable through
Hopf bifurcation. Especially, the first Hopf bifurcation value tends to that of
the ''average'' DDE model when the diffusion rate tends to infinity. Moreover,
we show that the direction of the Hopf bifurcation is forward, and the
bifurcating periodic solution from the first Hopf bifurcation value is
orbitally asymptotically stable, which improves the earlier result by Wei and
Li (Nonlinear. Anal., 60: 1351-1367, 2005)
Global Hopf bifurcation for differential-algebraic equations with state dependent delay
We develop a global Hopf bifurcation theory for differential equations with a
state-dependent delay governed by an algebraic equation, using the
-equivariant degree. We apply the global Hopf bifurcation theory to a
model of genetic regulatory dynamics with threshold type state-dependent delay
vanishing at the stationary state, for a description of the global continuation
of the periodic oscillations
Stability of equilibrium and periodic solutions of a delay equation modeling leukemia
We consider a delay differential equation that occurs in the study of chronic
myelogenous leukemia. After shortly reminding some previous results concerning
the stability of equilibrium solutions, we concentrate on the study of
stability of periodic solutions emerged by Hopf bifurcation from a certain
equilibrium point. We give the algorithm for approximating a center manifold at
a typical point (in the parameter space) of Hopf bifurcation (and an unstable
manifold in the vicinity of such a point, where such a manifold exists). Then
we find the normal form of the equation restricted to the center manifold, by
computing the first Lyapunov coefficient. The normal form allows us to
establish the stability properties of the periodic solutions occurred by Hopf
bifurcation
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