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Mechanisms of strange nonchaotic attractors in a nonsmooth system with border-collision bifurcations

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Abstract

It is not very clear to understand genesis and mechanisms for the creation of strange nonchaotic attractors (SNAs) due to the nonsmooth bifurcations in the nonsmooth systems. A quasiperiodically forced piecewise Logistic system is shown to exhibit many types of routes to the creation of SNAs. We point out that the truncation of border-collision torus-doubling bifurcation can lead to different types of SNAs. We identify and describe the Heagy–Hammel routes, fractalization route and intermittent routes after the two coexisting tori collide at the border and the doubled torus is interrupted in this system. It has been shown that there exist two critical tongue-type regions in the parameter space, where the different mechanisms for the birth of SNAs are investigated. These SNAs are identified by the Lyapunov exponents and the phase sensitivity exponents. Different types of SNAs are also characterized by the singular-continuous spectrum, Fourier transform, rational approximations, distribution of finite-time Lyapunov exponents and recurrence analysis.

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Acknowledgements

The authors are deeply indebted to all anonymous reviewers and the editor for their careful reading of the manuscript, as well as for their fruitful comments and advice which led to an improvement of this paper. This work was supported by the National Natural Science Foundation of China (Nos. 11732014, 11572205 and 11702111).

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  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, China

    Yunzhu Shen & Yongxiang Zhang

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Shen, Y., Zhang, Y. Mechanisms of strange nonchaotic attractors in a nonsmooth system with border-collision bifurcations. Nonlinear Dyn 96, 1405–1428 (2019). https://doi.org/10.1007/s11071-019-04862-5

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