Stochastic Hopf bifurcation in quasi-integrable-Hamiltonian systems

2004 ◽  
Vol 20 (5) ◽  
pp. 558-566 ◽  
Author(s):  
Gan Chunbiao
Keyword(s):  
Hopf Bifurcation ◽  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Stochastic Hopf Bifurcation

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 Two-Photon Algebra and Integrable Hamiltonian Systems

2001 ◽  
Vol 8 (sup1) ◽  
pp. 18-22 ◽  
Author(s):  
Angel Ballesteros ◽  
Francisco J Herranz
Keyword(s):  
Hamiltonian Systems ◽  
Integrable Hamiltonian Systems ◽  
Two Photon
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