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- V Gafiychuk, B Datsko, V Meleshko
- 2007

We study a fractional reaction-diffusion system with two types of variables: acti-vator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the… (More)

- V. V. Gafiychuk, B. Y. Datsko
- Applied Mathematics and Computation
- 2008

- V. V. Gafiychuk, B. Y. Datsko
- Computers & Mathematics with Applications
- 2010

- B. Y. Datsko, V. V. Gafiychuk
- Signal Processing
- 2011

The linear stability analysis is studied for a two-component fractional reaction-diffusion system with different derivative indices. Two different cases are considered when an activator index is larger than an inhibitor one and when an inhibitor variable index is larger than an activator one. General analysis is confirmed by computer simulation of the… (More)

- V V Gafiychuk, B Y Datsko
- Physical review. E, Statistical, nonlinear, and…
- 2007

The linear stage of stability is studied for a two-component fractional reaction-diffusion system. It is shown that, with a certain value of the fractional derivative index, a different type of instability occurs. The linear stability analysis shows that the system becomes unstable toward perturbations of finite wave number. As a result, inhomogeneous… (More)

- V V Gafiychuk, B Y Datsko
- Physical review. E, Statistical, nonlinear, and…
- 2008

The fractional reaction-diffusion system is investigated. The linear stage of the stability is studied for a two-component system with a different order of fractional derivatives for activator and inhibitor. Three different cases are considered: the derivative order for an activator is greater than that for an inhibitor, the inhibitor order derivative is… (More)

- B Y Datsko, V V Gafiychuk, I A Lubashevsky, A V Priezzhev
- Journal of medical engineering & technology
- 2006

We analyse necrosis growth due to thermal coagulation induced by laser light absorption and limited by heat diffusion into the surrounding live tissue. The tissue is assumed to contain a tumour in the undamaged tissue where the blood perfusion rate does not change during the action. By contrast, normal tissue responds strongly to an increase in the tissue… (More)

We analyze the effect of blood flow through large arteries of peripheral circulation on heat transfer in living tissue. Blood flow in such arteries gives rise to fast heat propagation over large scales, which is described in terms of heat superdiffusion. The corresponding bioheat heat equation is derived. In particular, we show that under local strong… (More)

- V V Gafiychuk, I A Lubashevsky, B Y Datsko
- Physical review. E, Statistical, nonlinear, and…
- 2005

We analyze the effect of blood flow through large arteries of peripheral circulation on heat transfer in living tissue. Blood flow in such arteries gives rise to fast heat propagation over large scales, which is described in terms of heat superdiffusion. The corresponding bioheat heat equation is derived. In particular, we show that under local strong… (More)