Conference publications

Abstracts

XVIII conference

Study of phase clusters in a distributed Selkov system

Verisokin A.Yu., Verveyko D.V., Postnikov E.B., Lavrova A.I.¹

Kursk state university, Russia, 305000, Kursk, Radishcheva, 33

¹Humboldt-Universität zu Berlin, Germany, D-12489 Berlin, Newtonstr. 15

1 pp. (accepted)

In this work we study glycolysis in the distributed medium and processes of synchronization. This research is the continuation of work [Лаврова А.И., Романовский Ю.М., Хайнрих Р., Шиманский-Гайер Л. , 2007]. The glycolytic reaction is defined by the modified two-variable Selkov model scheme extended with diffusion in the range of [0, 1]:

$$\\partial_{\tau}x=v-xy^2+D_1\partial^2_rx, \partial_{\tau}y=xy^2-wy+D_2\partial^2_ry.$$

The numerical simulations of synchronization processes are evaluated for the following values of reaction parameters: v=2.55 and w=2 (relaxation regime). We take the initial values for the considered distributed Selkov system in such a way that they present the values from one full limit cycle of a local oscillations with equispaced distribution of the Rayleigh phase [Lavrova A.I., Schimansky-Geier L., Postnikov E.B., 2009].

At the diffusion coefficients less than $10^{-4}$ we can observe the continuous cluster formation, at the large diffusion coefficients ($10^{-3}$) there is only one stage of clusterization and further synchronization, between these diffusion values the diffusion stabilized the distribution after several cascade iterations.

For the analysis of structure formation in the considered system, we use the Continuous Wavelet Transform with a wavelet from the Gaussian family. The maxima of this wavelet transform correspond to the points of fast phase change. This fact allows to find the hierarchical bifurcation cascade corresponding to the birth of phase clusters and to compare the points of cascade with the branch of fast relaxation motion on the limit cycle.

The obtained results allow to clear up the mechanism of formation of cluster regions observed in the experiment [Lavrova A.I., Bagyan S., Mair T., Hauser M.J.B. Schimansky-Geier L., 2009].

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