Amplitude equation formalism for reaction—subdiffusion systems | Zendy

Dmitry Alexeevich Zenyuk | Zendy; Georgii Gennadyevich Malinetskii | Zendy

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Amplitude equation formalism for reaction—subdiffusion systems

Author(s) -

Dmitry Alexeevich Zenyuk,

Georgii Gennadyevich Malinetskii

Publication year - 2021

Publication title -

keldysh institute preprints

Language(s) - English

Resource type - Journals

eISSN - 2071-2901

pISSN - 2071-2898

DOI - 10.20948/prepr-2021-93

Subject(s) - amplitude , formalism (music) , nonlinear system , differential equation , diffusion equation , anomalous diffusion , bifurcation , mathematical analysis , mathematics , fractional calculus , hopf bifurcation , physics , quantum mechanics , computer science , innovation diffusion , art , musical , knowledge management , economy , economics , visual arts , service (business)

The paper presents derivation of the amplitude equation for the Hopf bifurcation in the two-component system with nonlinear chemical kinetics and subdiffusion. Anomalous diffusion transport is described via Caputo fractional derivatives. The obtained amplitude equation is much more complex compared to the case of normal diffusion because solutions of fractional order linear differential equations have inconvenient behavior.

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