Bifurcations of self-similar solutions of the Fokker-Plank equations

F. Berezovskaya; G. Karev

doi:10.3934/proc.2005.2005.91

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2005, Volume 2005: 91-99. Doi: 10.3934/proc.2005.2005.91 open access

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Bifurcations of self-similar solutions of the Fokker-Plank equations

F. Berezovskaya^1, and
G. Karev^2,

1.
Department of Mathematics, Howard University, Washington D.C., 20059
2.
Oak Ridge Institute for Science and Education (ORISE) 8600 Rockville Pike, Bldg. 38A, Rm. 5N511N, Bethesda, MD 20894

Received: September 2004

Revised: May 2005

Published: August 2005

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Abstract

A class of one-dimensional Fokker-Plank equations having a common stationary solution, which is a power function of the state of the process, was found. We prove that these equations also have generalized self-similar solutions which describe the temporary transition from one stationary state to another. The study was motivated by problems arising in mathematical modeling of genome size evolution.

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Mathematics Subject Classification: Primary: 92B05.

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Bifurcations of self-similar solutions of the Fokker-Plank equations

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