In this paper,we develop a three-dimensional fractional-order cancer model.The proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector cells.The detailed analysis of the equilibrium points is studied.Also,the existence and uniqueness of the solution are investigated.The fractional derivative is considered in the Caputo sense.Numerical simulations are performed to illustrate the effectiveness of the obtained theoretical results.The outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic process.Further,the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed model.Also,it is observed from the obtained results that decrease in fractional-order p increases the chaotic behavior of the model.
We analyze the global structure and evolution of human gene coexpression networks driven by new gene integration. When the Pearson correlation coefficient is greater than or equal to 0.5, we find that the coexpression network consists of 334 small components and one "giant" connected subnet comprising of 6317 interacting genes. This network shows the properties of power-law degree distribution and small-world. The average clustering coefficient of younger genes is larger than that of the elderly genes(0.6685 vs. 0.5762). Particularly, we find that the younger genes with a larger degree also show a property of hierarchical architecture. The younger genes play an important role in the overall pivotability of the network and this network contains few redundant duplicate genes. Moreover, we find that gene duplication and orphan genes are two dominant evolutionary forces in shaping this network. Both the duplicate genes and orphan genes develop new links through a "rich-gets-richer"mechanism. With the gradual integration of new genes into the ancestral network, most of the topological structure features of the network would gradually increase. However, the exponent of degree distribution and modularity coefficient of the whole network do not change significantly, which implies that the evolution of coexpression networks maintains the hierarchical and modular structures in human ancestors.
Jian ZuYuexi GuYu LiChentong LiWenyu ZhangYong E.ZhangUnJin LeeLi ZhangManyuan Long
