Eur. Phys. J. Special Topics 229, 3033–3042 (2020)
https://doi.org/10.1140/epjst/e2020-000070-y

Regular Article

Suppression of self-oscillations and formation of heterogeneous structures by diffusion in the non-linear glycolytic model

Ural Mathematical Center, Ural Federal University, Lenina avenue, 51, Ekaterinburg 620000, Russia

^a e-mail: irina.bashkirtseva@urfu.ru

Received: 22 April 2020
Accepted: 9 September 2020
Published online: 19 November 2020

Abstract

A dynamical distributed model of glycolysis with the diffusion is considered in the parametric zone of self-oscillations. A phenomenon of the diffusion-induced suppression of self-oscillations is found and studied by technique of harmonic coefficients. We show how, under increase of diffusion, temporal oscillations of homogeneous solutions transform into stationary non-homogeneous structures in the form of patterns-attractors. A phenomenon of multistability in this spatially distributed glycolytic model is discussed and a variety of coexisting patterns and their amplitude characteristics is quantified.