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Analysis of instabilities and pattern formation in time fractional reaction-diffusion systems | | B.Y. Datsko
; V.V. Gafiychuk
; | | Date: |
8 Dec 2009 | | Abstract: | We analyzed conditions for Hopf and Turing instabilities to occur in
two-component fractional reaction-diffusion systems. We showed that the
eigenvalue spectrum and fractional derivative order mainly determine the type
of instability and the dynamics of the system. The results of the linear
stability analysis are confirmed by computer simulation of the model with cubic
nonlinearity for activator variable and linear dependance for the inhibitor
one. It is shown that pattern formation conditions of instability and transient
dynamics are different than for a standard system. As a result, more
complicated pattern formation dynamics takes place in fractional
reaction-diffusion systems. | | Source: | arXiv, 0912.1500 | | Services: | Forum | Review | PDF | Favorites | |
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