Pattern dynamics of network-organized system with cross-diffusion

doi:10.1088/1674-1056/26/2/020501

中国物理B ›› 2017, Vol. 26 ›› Issue (2): 20501-020501.doi: 10.1088/1674-1056/26/2/020501

Pattern dynamics of network-organized system with cross-diffusion

Qianqian Zheng(郑前前), Zhijie Wang(王直杰), Jianwei Shen(申建伟)

1 College of Information Science and Technology, Donghua University, Shanghai 201620, China;
2 Institute of Applied Mathematics, Xuchang University, Xuchang 461000, China

收稿日期:2016-07-23 修回日期:2016-11-20 出版日期:2017-02-05 发布日期:2017-02-05
通讯作者: Zhijie Wang, Jianwei Shen E-mail:wangzj@dhu.edu.cn;phdshen@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272277, 11572278, and 11572084) and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province, China (Grant No. 2017JR0013).

Pattern dynamics of network-organized system with cross-diffusion

Qianqian Zheng(郑前前)¹, Zhijie Wang(王直杰)¹, Jianwei Shen(申建伟)²

1 College of Information Science and Technology, Donghua University, Shanghai 201620, China;
2 Institute of Applied Mathematics, Xuchang University, Xuchang 461000, China

Received:2016-07-23 Revised:2016-11-20 Online:2017-02-05 Published:2017-02-05
Contact: Zhijie Wang, Jianwei Shen E-mail:wangzj@dhu.edu.cn;phdshen@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272277, 11572278, and 11572084) and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province, China (Grant No. 2017JR0013).

摘要/Abstract

摘要： Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction-diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.

关键词: cross diffusion, random network, Turing instability, amplitude equation

Abstract: Cross-diffusion is a ubiquitous phenomenon in complex networks, but it is often neglected in the study of reaction-diffusion networks. In fact, network connections are often random. In this paper, we investigate pattern dynamics of random networks with cross-diffusion by using the method of network analysis and obtain a condition under which the network loses stability and Turing bifurcation occurs. In addition, we also derive the amplitude equation for the network and prove the stability of the amplitude equation which is also an effective tool to investigate pattern dynamics of the random network with cross diffusion. In the meantime, the pattern formation consistently matches the stability of the system and the amplitude equation is verified by simulations. A novel approach to the investigation of specific real systems was presented in this paper. Finally, the example and simulation used in this paper validate our theoretical results.

Key words: cross diffusion, random network, Turing instability, amplitude equation

中图分类号: (Computational methods in statistical physics and nonlinear dynamics)

05.10.-a

05.40.Ca (Noise) 05.65.+b (Self-organized systems) 05.70.Ln (Nonequilibrium and irreversible thermodynamics)

郑前前, 王直杰, 申建伟. Pattern dynamics of network-organized system with cross-diffusion[J]. 中国物理B, 2017, 26(2): 20501-020501.

Qianqian Zheng(郑前前), Zhijie Wang(王直杰), Jianwei Shen(申建伟). Pattern dynamics of network-organized system with cross-diffusion[J]. Chin. Phys. B, 2017, 26(2): 20501-020501.

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Pattern dynamics of network-organized system with cross-diffusion

Pattern dynamics of network-organized system with cross-diffusion

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