https://oldena.lpnu.ua/handle/ntb/42389| Title: | Amplitude equations for activator-inhibitor system with superdiffusion |
| Other Titles: | Амплiтуднi рiвняння для системи типу активатор-iнгiбiтор iз супердифузiєю |
| Authors: | Prytula, Z. |
| Affiliation: | Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine |
| Bibliographic description (Ukraine): | Prytula Z. Amplitude equations for activator-inhibitor system with superdiffusion / Z. Prytula // Mathematical Modeling and Сomputing. – 2016. – Volume 3, number 2. – Р. 191–198. – Bibliography: 23 titles. |
| Journal/Collection: | Mathematical Modeling and Сomputing |
| Issue Date: | 2016 |
| Country (code): | UA |
| UDC: | 517.519+517.96 |
| Keywords: | reaction-diffusion system cubic nonlinearity fractional operator superdiffusion система реакцiї-дифузiї кубiчна нелiнiйнiсть дробовий оператор супердифузiя |
| Number of pages: | 191–198 |
| Abstract: | The generalized activator-inhibitor model with cubic nonlinearity, in which the classical Laplacian is replaced by fractional operator has been studied. The fractional operator reflects the nonlocal behavior of superdiffusion. A spatially homogeneous, time independent solution has been found and its linear stability was studied. We have also performed a weakly nonlinear analysis and obtained a system of amplitude equations that are the basis for analysing pattern formation as well as parameter regimes for which various steady-state patterns would exist. Дослiджено узагальнену модель типу активатор-iнгiбiтор iз кубiчною нелiнiйнiстю, в якiй класичний оператор Лапласа замiнено дробовим аналогом. Дробовий оператор вiдображує нелокальну поведiнку супердифузiї. Знайдено просторово-однорiдний стацiонарний розв’язок та вивчено його лiнiйну стiйкiсть. Проведено також слабконелiнiйний аналiз та отримано систему амплiтудних рiвнянь. Отриманi рiвняння дають можливiсть аналiзувати типи структур, якi виникають у розглядуванiй реакцiйнодифузiйнiй системi. |
| URI: | https://ena.lpnu.ua/handle/ntb/42389 |
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| Content type: | Article |
| Appears in Collections: | Mathematical Modeling And Computing. – 2016. – Vol. 3, No. 2 |
| File | Description | Size | Format | |
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| 010-83-90.pdf | 230.9 kB | Adobe PDF | View/Open |
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