Title: On the maximum number of periodic solutions for higher dimensional systems
Department: Department of Mathematics, Shanghai Normal University Shanghai, 200234, P.R.China
Abstract: In this paper, we study the problem of the maximum number of zeros of vector analytic real functions with a small parameter based on higher dimensional generalization of Rouche's theorem from complex analysis. Then using the obtained result we study the maximum number of periodic solutions for higher dimensional systems.
Finally we present an application to autonomous systems. .
Key words: Averaging method; bifurcation function; periodic solution.
