Theory of rotated equations and applications to a population model

By Maoan Han, Xiaoyan Hou, Lijuan Sheng, Chaoyang Wang. 2018

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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.

Subfields: Mathematical Physics, Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8e253864215ba6ad93c9c658acf9edb0de89466d