期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
卷 20, 期 4, 页码 1107-1116出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2015.20.1107
关键词
Epidemic model; Bogdanov-Takens bifurcation; codimension three
资金
- [NSFC-11171267]
- [NSFC-11271027]
- [NSFC-11371369]
- [NMSRC-2012ZX10001-001]
It was shown in [11] that in an epidemic model with a nonlinear incidence and two compartments some complex dynamics can appear, such as the backward bifurcation, codimension 1 Hopf bifurcation and codimension 2 Bogdanov-Takens bifurcation. In this paper we prove that for the same model the codimension of Bogdanov-Takens bifurcation can be 3 and is at most 3. Hence, more complex new phenomena, such as codimension 2 Hopf bifurcation, codimension 2 homoclinic bifurcation and semi-stable limit cycle bifurcation, exhibit. Especially, the system can have and at most have 2 limit cycles near the positive singularity.
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