caa a22 4500 465811442 CHVBK 20180323112117.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF02108203 doi (NATIONALLICENCE)springer-10.1007/BF02108203 Zhiming Zheng Department of Mathematics, Peking University, China aut Qualitative analysis of van der pol type equation with periodic forcing term [Elektronische Daten] [Zheng Zhiming] In this paper we analyze the qualitative behaviour of the equation $$\varepsilon \ddot X + q(X) \dot X + \varepsilon X = b p (t)$$ , whereε is a small parameter. We divide the interval of parameterb into four sets of subintervals.A, B, C andD. Forb∈A, B orD, we discuss the different structures of the attractors of the equation and their stabilities. When chaotic phenomena appear, we also estimate the entropy. Forb∈C, the set of bifurcation intervals, we analyze the bifurcating type and get a series of consequences from the results of Newhouse and Palis. Springer-Verlag, 1990 Acta Mathematica Sinica Springer-Verlag 6/3(1990-09-01), 243-256 1439-8516 6:3<243 1990 6 10114 https://doi.org/10.1007/BF02108203 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02108203 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zhiming Zheng Department of Mathematics, Peking University, China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica Springer-Verlag 6/3(1990-09-01), 243-256 1439-8516 6:3<243 1990 6 10114 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer