About the Authors

Fang Yan

Affiliations Department of Mathematics, Shanghai University, Shanghai, P. R. China, Institute of System Biology, Shanghai University, Shanghai, P. R. China

Haihong Liu

Affiliation Department of Mathematics, Yunnan Normal University, Kunming, P. R. China

Junjun Hao

Affiliation Institute of System Biology, Shanghai University, Shanghai, P. R. China

Zengrong Liu

zrongliu@126.com

Affiliations Department of Mathematics, Shanghai University, Shanghai, P. R. China, Institute of System Biology, Shanghai University, Shanghai, P. R. China

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: FY ZRL. Performed the experiments: FY HHL ZRL. Analyzed the data: FY HHL JJH ZRL. Contributed reagents/materials/analysis tools: FY HHL JJH ZRL. Wrote the paper: FY HHL JJH ZRL.