论文信息 - Qualitative analysis of van der pol type equation with periodic forcing term

Qualitative analysis of van der pol type equation with periodic forcing term

AbstractIn 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.

Zheng Zhiming | Z. Zhiming

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