Pattern Formation In The Cancer Network Mediated By Small RNA

In this paper,spontaneous pattern formation in the di?usive cancer network mediated by small RNA has been well studied.And we obtain the critical line of Hopf and Turing bifurcation in the spatial domain. In the mean time,we also derive the amplitude equation by using the Taylor series expansion, multi scaling and further expansion in power of a small parameter in the cases of Hopf and Turing instabilities, and apply this analysis to the di?usive cancer network. As the results, we obtain the explicit condition on how the dynamics of the di?usive cancer network in which the miRNA cluster and the protein(target transcript factor). These results reveal that this system has rich dynamics, such as spotted stripe and hexagon patterns. Finally,the numerical simulation shows that the analytical results agree with numerical simulation.