Amplitude equations for activator-inhibitor system with superdiffusion
| dc.citation.journalTitle | Mathematical Modeling and Сomputing | |
| dc.contributor.affiliation | Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine | uk_UA |
| dc.contributor.author | Prytula, Z. | |
| dc.coverage.country | UA | uk_UA |
| dc.date.accessioned | 2018-07-11T20:32:15Z | |
| dc.date.available | 2018-07-11T20:32:15Z | |
| dc.date.issued | 2016 | |
| dc.description.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. | uk_UA |
| dc.format.pages | 191–198 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/42389 | |
| dc.language.iso | en | uk_UA |
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| dc.subject | reaction-diffusion system | uk_UA |
| dc.subject | cubic nonlinearity | uk_UA |
| dc.subject | fractional operator | uk_UA |
| dc.subject | superdiffusion | uk_UA |
| dc.subject | система реакцiї-дифузiї | uk_UA |
| dc.subject | кубiчна нелiнiйнiсть | uk_UA |
| dc.subject | дробовий оператор | uk_UA |
| dc.subject | супердифузiя | uk_UA |
| dc.subject.udc | 517.519+517.96 | uk_UA |
| dc.title | Amplitude equations for activator-inhibitor system with superdiffusion | uk_UA |
| dc.title.alternative | Амплiтуднi рiвняння для системи типу активатор-iнгiбiтор iз супердифузiєю | uk_UA |
| dc.type | Article | uk_UA |