About the Authors

Zhi-Qiang Xia

Affiliations Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, PR China, Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, PR China

Juan Zhang

Affiliation Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, PR China

Ya-Kui Xue

xyk5152@163.com (YKX); gquansun@126.com (GQS); jinzhn@263.net (ZJ)

Affiliation Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, PR China

Gui-Quan Sun

xyk5152@163.com (YKX); gquansun@126.com (GQS); jinzhn@263.net (ZJ)

Affiliation Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, PR China

Zhen Jin

xyk5152@163.com (YKX); gquansun@126.com (GQS); jinzhn@263.net (ZJ)

Affiliation Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, PR China

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: JZ GQS. Performed the experiments: ZQX JZ. Analyzed the data: ZQX JZ. Contributed reagents/materials/analysis tools: YKX GQS ZJ. Wrote the paper: ZQX GQS ZJ.