Stability and Bifurcation in the Harmonic Oscillator with Multiple, Delayed Feedback Loops
نویسنده
چکیده
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 strengths of the two feedback loops. The bifurcations which occur when stability is lost are described and the location of Hopf-Hopf and Hopf-steady state bifurcation interactions are given. Numerical simulations reveal the presence of quasiperiodic solutions and multistability near such codimension two bifurcation points.
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