Hopf bifurcation and multiple periodic solutions in a damped harmonic oscillator with delayed feedback
نویسندگان
چکیده
منابع مشابه
Stability and Bifurcation in the Harmonic Oscillator with Multiple, Delayed Feedback Loops
We analyze the second order diierential equation describing a damped harmonic oscillator with nonlinear feedback depending on both the state and the derivative of the state at some time in the past. The characteristic equation for the linear stability of the equilibrium is completely solved, and the stability region is illustrated in a parameter space consisting of the time delay and the streng...
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A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanic...
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The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The results are used to compare delayed versus undelayed feedback, as well as discrete versus distributed delays. Conditions are obtained for which delayed feedback...
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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 ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2013.11.015