Asymptotic behavior of a discrete turing model

Hunseok Kang

doi:10.3934/dcds.2010.27.265

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2010, Volume 27, Issue 1: 265-284. Doi: 10.3934/dcds.2010.27.265

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Asymptotic behavior of a discrete turing model

Hunseok Kang^1,

1.
Research Institute for Electronic Science, Hokkaido University, Kita-20, Nishi-10, Kita-ku, Sapporo 001-0020

Received: March 31, 2009

Revised: September 30, 2009

Published: February 2010

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Abstract

In this paper, we discuss a discrete version of the Turing continuous model of morphogenesis. We describe some dynamical properties of the asymptotic behaviors for trajectories escaping to infinity and those which remain bounded, and find various types of invariant sets of trajectories in this system. Finally, some numerical results of asymptotic behaviors of trajectories are presented.

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Mathematics Subject Classification: Primary: 37N25, 37N10; Secondary: 35K57.

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