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Coexistence of Strange Nonchaotic Attractors in a Quasiperiodically Forced Dynamical Map

Yunzhu Shen

School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P. R. China

E-mail Address: jdshenyunzhu@163.com

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Yongxiang Zhang

http://orcid.org/0000-0001-6694-482X

School of Mathematics and Statistics, Qingdao University, Qingdao 266071, P. R. China

E-mail Address: zyx9701@126.com

Corresponding author.

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, and

Sajad Jafari

Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran

E-mail Address: sajadjafari83@gmail.com

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https://doi.org/10.1142/S0218127420501837Cited by:8 (Source: Crossref)

Abstract

In this paper, we investigate coexisting strange nonchaotic attractors (SNAs) in a quasiperiodically forced system. We also describe the basins of attraction for coexisting attractors and identify the mechanism for the creation of coexisting attractors. We find three types of routes to coexisting SNAs, including intermittent route, Heagy–Hammel route and fractalization route. The mechanisms for the creation of coexisting SNAs are investigated by the interruption of coexisting torus-doubling bifurcations. We characterize SNAs by the largest Lyapunov exponents, phase sensitivity exponents and power spectrum. Besides, the SNAs with extremely fractal basins exhibit sensitive dependence on the initial condition for some particular parameters.

Keywords:

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