First passage failure of MDOF quasi-integrable Hamiltonian systems with fractional derivative damping

2011 ◽  
Vol 222 (3-4) ◽  
pp. 245-260 ◽  
Author(s):  
Lincong Chen ◽  
Qingqu Zhuang ◽  
Weiqiu Zhu
Keyword(s):  
Fractional Derivative ◽  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
First Passage ◽  
First Passage Failure ◽  
Fractional Derivative Damping

STOCHASTIC HOPF BIFURCATION OF QUASI-INTEGRABLE HAMILTONIAN SYSTEMS WITH FRACTIONAL DERIVATIVE DAMPING

2012 ◽  
Vol 22 (04) ◽  
pp. 1250083 ◽  
Author(s):  
F. HU ◽  
W. Q. ZHU ◽  
L. C. CHEN
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Hamiltonian Systems ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Bifurcation Parameter ◽  
Integrable Hamiltonian Systems ◽  
Fractional Derivative Damping ◽  
Stochastic Hopf Bifurcation

The stochastic Hopf bifurcation of multi-degree-of-freedom (MDOF) quasi-integrable Hamiltonian systems with fractional derivative damping is investigated. First, the averaged Itô stochastic differential equations for n motion integrals are obtained by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, an expression for the average bifurcation parameter of the averaged system is obtained and a criterion for determining the stochastic Hopf bifurcation of the system by using the average bifurcation parameter is proposed. An example is given to illustrate the proposed procedure in detail and the numerical results show the effect of fractional derivative order on the stochastic Hopf bifurcation.

scholarly journals First-Passage Failure of Quasi-Integrable Hamiltonian Systems

2002 ◽  
Vol 69 (3) ◽  
pp. 274-282 ◽  
Author(s):  
W. Q. Zhu ◽  
M. L. Deng ◽  
Z. L. Huang
Keyword(s):  
Hamiltonian Systems ◽  
First Passage Time ◽  
Digital Simulation ◽  
Reliability Function ◽  
Passage Time ◽  
Kolmogorov Equation ◽  
Conditional Probability Density ◽  
Integrable Hamiltonian Systems ◽  
First Passage ◽  
First Passage Failure

The first-passage failure of quasi-integrable Hamiltonian systems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito^ stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamitonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

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