Hopf bifurcation analysis of a general non-linear differential equation with delay
نویسندگان
چکیده
منابع مشابه
Stability and Hopf Bifurcation Analysis of the Delay Logistic Equation
Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any biological system, we seek to analyse the effect of delays on the growth of populations governed by the logistic equation. In this paper, the local stability...
متن کاملSingular 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 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 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 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: Journal of Computational and Applied Mathematics
سال: 2013
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.06.029