Pattern dynamics of network-organized system with cross-diffusion

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

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.

Keywords: cross diffusion random network Turing instability amplitude equation

Received: 23 July 2016
Revised: 20 November 2016
Accepted manuscript online:

PACS:	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)
	05.40.Ca	(Noise)
	05.65.+b	(Self-organized systems)
	05.70.Ln	(Nonequilibrium and irreversible thermodynamics)

Fund: 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).

Corresponding Authors: Zhijie Wang, Jianwei Shen
E-mail: wangzj@dhu.edu.cn;phdshen@126.com

Cite this article:

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

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