Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634923 | Applied Mathematics and Computation | 2008 | 10 Pages |
Abstract
We investigate inhomogeneous oscillatory instability conditions in fractional reaction-diffusion systems. It is shown that non-linear stationary solutions emerge as a result of Turing instability becoming unstable according to oscillatory perturbation and transform to inhomogeneous oscillatory structures. It is also shown that with the certain value of the fractional derivatives index, a new type of instability takes place and the system becomes unstable towards perturbations of finite wave number. As a result, oscillatory perturbations with this wave number become unstable and lead to non-linear oscillations which result in spatial oscillatory structure formation. Computer simulation of a Bonhoeffer-van der Pol type reaction-diffusion systems with fractional time derivatives is performed.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
V. Gafiychuk, B. Datsko,