期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 38, 期 4, 页码 2171-2185出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2018089
关键词
Periodic solution; rotated equation; saddle-node bifurcation
资金
- National Natural Science Foundation of China [11431008, 11771296]
We consider a family of scalar periodic equations with a parameter and establish theory of rotated equations, studying the behavior of periodic solutions with the change of the parameter. It is shown that a stable (completely unstable) periodic solution of a rotated equation varies monotonically with respect to the parameter and a semi-stable periodic solution splits into two periodic solutions or disappears as the parameter changes in one direction or another. As an application of the obtained results, we give a further study of a piecewise smooth population model verifying the existence of saddle-node bifurcation.
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