Singular Hopf bifurcation in a differential equation with large state-dependent delay
نویسندگان
چکیده
منابع مشابه
Singular Hopf bifurcation in a differential equation with large state-dependent delay.
We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawt...
متن کاملStability and Hopf Bifurcation in Differential Equations with One Delay
A class of parameter dependent differential equations with one delay is considered. A decomposition of the parameter space into domains where the corresponding characteristic equation has a constant number of zeros with positive real part is provided. The local stability analysis of the zero solution and the computation of all Hopf bifurcation points with respect to the delay is given.
متن کاملSubcritical Hopf bifurcation in dynamical systems described by a scalar nonlinear delay differential equation.
A subcritical Hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally. The subcritical Hopf bifurcation leads to a significant domain of bistability where stable steady and time-periodic states coexist.
متن کاملDelayed feedback control of a delay equation at Hopf bifurcation
We embark on a case study for the scalar delay equation ẋ(t) = λf(x(t− 1)) + b−1(x(t− θ) + x(t− θ− p/2)) with odd nonlinearity f , real nonzero parameters λ, b, and three positive time delays 1, θ, p/2. We assume supercritical Hopf bifurcation from x ≡ 0 in the well-understood single-delay case b = ∞. Normalizing f ′(0) = 1, branches of constant minimal period pk = 2π/ωk are known to bifurcate ...
متن کاملStability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay
We propose a mathematical model describing the dynamics of a hematopoietic stem cell population. The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a Lyapunov–Razumikhi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2014
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.2013.0596