Abstract
The stochastic Hopf bifurcation of multi-degree-of-freedom (MDOF) quasi-integrable Hamiltonian systems with multi-time-delayed feedback control subject to wide-band noise excitations is studied. First, the time-delayed feedback control forces are expressed approximately in terms of the system state variables without time delay and the system is converted into an ordinary quasi-integrable Hamiltonian system. The averaged Itô stochastic differential equations are derived by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then the expression for average bifurcation parameter of the averaged system is obtained approximately and a criterion for determining the stochastic Hopf bifurcation induced by time-delayed feedback control forces in the original system using average bifurcation parameter is proposed. An example is worked out in detail to illustrate the criterion and its validity and to show the effect of time delay in feedback control on stochastic Hopf bifurcation of the system.
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Liu, Z.H., Zhu, W.Q. Stochastic Hopf bifurcation of quasi-integrable Hamiltonian systems with multi-time-delayed feedback control and wide-band noise excitations. Nonlinear Dyn 69, 935–947 (2012). https://doi.org/10.1007/s11071-011-0315-9
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DOI: https://doi.org/10.1007/s11071-011-0315-9