关键词: Hopf分岔, Pitchfork分岔, 吸引域, 极限环

Abstract: We studied the bifurcation behaviors of equilibrium points and limit cycles as well as attraction domain of equilibrium state of a modified wing model. The results show that bifurcation structure of equilibrium state is affected by the coefficients of the structural restoring moment so that two pairs of nontrivial equilibrium points with opposite stability coexist or vanish due to the simultaneous occurrence of Fold bifurcations. The attraction domains exhibit a centrosymmetric structural distribution when some initial components are fixed. When the frequency ratio is used as a bifurcation parameter, the trivial equilibrium point loses stability due to Hopf bifurcation, and the stable limit cycles undergo a Pitchfork bifurcation to produce two stable limit cycles. With further reduction of the frequency ratio, two coexisting limit cycles simultaneously undergo a Neimmark-Sacker bifurca
tion, leading to two stable two-dimensional toruses.

Key words: Hopf bifurcation, Pitchfork bifurcation, attraction domain, limit cycle