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THE EXISTENCE OF LIMIT CYCLES FOR THE SYSTEM X=Q(x,y),Y=P(x)

THE EXISTENCE OF LIMIT CYCLES FORTHE SYSTEM x = Q(x ,y) , y = P(x)
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摘要 In [1], by a transformation on the Liemrd equation system suchihai the trajectories of (1)on both left and right half -planes change into thoseintegral curves of the new equation system merely on the right half-plane,A.F.Hilippov shows that under some certain conditions the stable limit cycles of system (1)must exist.Applying the Filippov’s method on the more generalized systemthis paper provides a sufficient condition for the existence of the stable limit cycles oftvstem (2). In [1], by a transformation on the Liemrd equation system suchihai the trajectories of (1)on both left and right half -planes change into thoseintegral curves of the new equation system merely on the right half-plane,A.F.Hilippov shows that under some certain conditions the stable limit cycles of system (1)must exist.Applying the Filippov’s method on the more generalized systemthis paper provides a sufficient condition for the existence of the stable limit cycles oftvstem (2).
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第1期59-66,共8页 应用数学和力学(英文版)
关键词 limit cycle. trajectory.annular region inner(outer) boundary limit cycle. trajectory.annular region, inner(outer) boundary
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