Abstract
This chapter investigates a specific point of the very intricate asymptotic behaviour of the SD oscillator , which is known as the Wada basin dynamics. The oscillator is subjected to a linear viscous damping and to a sinusoidal forcing. As described and already observed through direct numerical integration, this system may possess more than twenty coexisted low-period periodic attractors for a given set of parameters. The large number of stable orbits yields a complex structure of closely interwoven basins of attraction. We obtain the so-called Wada basins of which the boundaries are rigorously described.
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Notes
- 1.
This chapter is due to the contribution by Professor Yongxiang Zhang, Shenyang Agricultural University, College of Science, Shenyang, Liaoning, China, Professors Guanwei Luo, Gansu Key Laboratory for System Dynamics and Reliability of Railway Transportation Equipment, Lanzhou Jiaotong University, Lanzhou, China and Doctor Mei Lin, The Engineering Institute, Air Engineering Univesity, Xi’an, Shanxi, China.
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Cao, Q., Léger, A. (2017). Wada Basin Dynamics. In: A Smooth and Discontinuous Oscillator. Springer Tracts in Mechanical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53094-8_6
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