Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 22, Issue 3, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127412500575
Keywords
Limit cycle; nonsmooth system; Lienard system; Hopf bifurcation; parabolic-parabolic type; focus-focus type; focus-parabolic type
Funding
- National Natural Science Foundation of China [10971139]
- Ministry of Education [20103127110001]
- Natural Science Foundation of Education Department of Anhui Province [KJ2010B353]
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In this paper, we mainly discuss Hopf bifurcation for planar nonsmooth general systems and Lienard systems with foci of parabolic-parabolic (PP) or focus-parabolic (FP) type. For the bifurcation near a focus, when the focus is kept fixed under perturbations we prove that there are at most k limit cycles which can be produced from an elementary weak focus of order 2k + 2 (resp. k + 1)(k >= 1) if the focus is of PP (resp. FP) type, and we present the conditions to ensure these upper bounds are achievable. For the bifurcation near a center, the Hopf cyclicicy is studied for these systems. Some interesting applications are presented.
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