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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, China

    Zheng Zhiming

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  1. Zheng Zhiming
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Zhiming, Z. Qualitative analysis of van der pol type equation with periodic forcing term. Acta Mathematica Sinica 6, 243–256 (1990). https://doi.org/10.1007/BF02108203

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  • DOI: https://doi.org/10.1007/BF02108203

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