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Coexistence of attractors and effects of noise on coupled piecewise maps

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Abstract

The synchronization transition in coupled piecewise map lattices is studied. The average order parameter is calculated to diagnose synchronization of coupled piecewise maps. As a result, it shows that coexistence of a period cluster and synchronization states in the synchronization transition process. A detailed research shows that the period clusters consist of two coexisting period attractors, and their period orbit is an unstable periodic orbit of the isolate map. The unstable periodic orbit is stabilized again by the mutual interactions of the local nonlinearity and the spatial coupling. The influence of noise on the complete synchronization (CS) in coupled piecewise map systems is also studied in this work. Synchronization probability densities and average order parameters as a function of the coupling strength with various noise intensities are calculated. When the noise intensity is small, the noise can postpone synchronization transition processes. However, if the noise intensity is larger, the noise can destroy the period clusters states, shorten the synchronization transition and enhance the CS in coupled piecewise maps.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No.11205006), the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 12JK0962), and the Natural Science New Star of Science and Technologies Research Plan in Shaanxi Province of China (Grant No. 2014KJXX-77).

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  1. Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji, 721016, China

    Ke-Li Yang & Can-Jun Wang

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  1. Ke-Li Yang
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Correspondence to Ke-Li Yang.

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Yang, KL., Wang, CJ. Coexistence of attractors and effects of noise on coupled piecewise maps. Nonlinear Dyn 79, 377–385 (2015). https://doi.org/10.1007/s11071-014-1671-z

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