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- 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
- Computers & Mathematics with Applications
- 2010

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

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

The linear stability analysis is studied for a two-component fractional reactiondiffusion 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 system… (More)

- Ihor Lubashevsky, B. Y. Datsko
- CogSci
- 2014

We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of new memory traces caused by learning a certain fragment of information pattern and affected by the fragments of this… (More)

- Roman Andrushkiw, V. V. Gafiychuk, B. Y. Datsko
- Mathematical and Computer Modelling
- 2007

- B. Y. Datsko, Yury F. Luchko, V. V. Gafiychuk
- I. J. Bifurcation and Chaos
- 2012

- 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)

- 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)