KIAM Main page Web Library  •  Publication Searh  Ðóññêèé 
Publication

KIAM Preprint ¹ 98, Moscow, 2019
Authors: Zenyuk D. A., Malinetskii G.G.
One-dimensional Brusselator with time-fractional derivative
Abstract:
In the present paper possible scenarios of pattern formation in non-linear media with diffusion and differential operators of non-integer order are studied for the abstract Brusselator model. By means of the standard linear analysis exact critical values for different types of instabilities are derived. It is shown that stability criteria significantly depend on the order of the fractional derivative in case of the Hopf and C2TH bifurcations. Predictions of the linear theory are confirmed by numerical simulation. The exposition is accompanied by a concise survey of the main results in the fields of fractional calculus and dynamical systems of non-integer order.
Keywords:
fractional calculus, reaction—diffusion systems
Publication language: russian,  pages: 32
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
Export link to publication in format:   RIS    BibTeX
View statistics (updated once a day)
over the last 30 days — 17 (+8), total hit from 01.11.2019 — 590
About authors:
  • Zenyuk Dmitry Alexeevich,  orcid.org/0000-0003-3383-6878KIAM RAS
  • Malinetskii Georgii Gennadyevich,  orcid.org/0000-0001-6041-1926KIAM RAS