TY - JOUR
T1 - Stochastic bifurcation in duffing system subject to harmonic excitation and in presence of random noise
AU - Xu, Wei
AU - He, Qun
AU - Fang, Tong
AU - Rong, Haiwu
PY - 2004/11
Y1 - 2004/11
N2 - A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.
AB - A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.
KW - Digraph
KW - Duffing system
KW - Global analysis
KW - Stochastic attractor
KW - Stochastic bifurcation
KW - Stochastic saddle
KW - The generalized cell mapping method
UR - http://www.scopus.com/inward/record.url?scp=2442449276&partnerID=8YFLogxK
U2 - 10.1016/j.ijnonlinmec.2004.02.009
DO - 10.1016/j.ijnonlinmec.2004.02.009
M3 - 文章
AN - SCOPUS:2442449276
SN - 0020-7462
VL - 39
SP - 1473
EP - 1479
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
IS - 9
ER -