Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise

International Journal of Non-Linear Mechanics

Volumn 39, Issue 9, 2004, Pages 1473-1479

  Xu, Wei ^a   He, Qun ^a,b   Fang, Tong ^a   Rong, Haiwu ^c  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b Engineering College of Armed Police Force   (China)

^c Foshan Inst of Sci and Technology   (China)

Author keywords

Digraph; Duffing system; Global analysis; Stochastic attractor; Stochastic bifurcation; Stochastic saddle; The generalized cell mapping method

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; ENERGY DISSIPATION; HARMONIC ANALYSIS; LYAPUNOV METHODS; PARAMETER ESTIMATION; RANDOM PROCESSES; TOPOLOGY;

DIGRAPH; DUFFING SYSTEM; GLOBAL ANALYSIS; STOCHASTIC ATTRACTOR; STOCHASTIC BIFURCATION; STOCHASTIC SADDLE; THE GENERALIZED CELL MAPPING SYSTEM;

NONLINEAR SYSTEMS;

EID: 2442449276     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2004.02.009     Document Type: Conference Paper

References (14)

1. Arnold L. Random Dynamical Systems. 1998;Springer, New York.
2. Baxendale P. Asymptotic behavior of stochastic flows of diffeomorphisms. Ito K., Hida T. Stochastic Processes and Their Applications. Lecture Notes in Mathematics. Vol. 1203:1986;1-19 Springer, Berlin, Heidelberg, New York.
3. Meunier C., Verga A.D. Noise and bifurcation. J. Stat. Phys. 50:1988;345-375.
4. Crauel H., Flandoli F. Additive noise destroys a pitchfork bifurcation. J. Dyn. Differential Equations. 10:1998;259-274.
5. Hsu C.S. A theory of cell to cell mapping dynamical systems. ASME J. Appl. Mech. 47:1980;931-939.
6. Tongue B.H., Gu K.Q. A higher order method of interpolated cell mapping. J. Sound Vib. 125:1988;169-179.
7. Hsu C.S. A generalized theory of cell to cell mapping for nonlinear dynamical systems. ASME J. Appl. Mech. 53:1981;695-701.
8. Sun J.Q., Hsu C.S. The generalized cell mapping method in nonlinear random vibration based upon short-time Gaussian approximation. J. Appl. Mech. 57:1990;1018-1025.
9. Sun J.Q. Random vibration analysis of a non-linear system with dry friction damping by the short-time Gaussian cell mapping method. J. Sound Vib. 180:1995;785-795.
10. Guder R., Kreuzer E. Using generalized cell mapping to approximate invariant measures on compact manifolds. Int. J. Bifurcation Chaos. 7:1999;2487-2499.
11. Hsu C.S. Global analysis of dynamical systems using posets and digraphs. Int. J. Bifurcation Chaos. 5:1995;1085-1118.
12. Hong, Ling, Xu, Jianxue, Crises and chaotic transient by the generalized cell mapping digraph method, Phys. Lett. A 262 (1999) 361-375.
13. Hong, Ling, Xu, Jianxue, Discontinuous bifurcations of chaotic attractors in forced oscillators by generalized cell mapping digraph (GCMD) method, Int. J. Bifurcation Chaos 11 (2001) 723-736.
14. Zhu W.Q., Lu M.Q., Wu Q.T. Stochastic jump and bifurcation of a Duffing oscillator under narrow-band excitation. J. Sound Vib. 165:1993;285-304.