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February  2010, 27(1): 265-284. doi: 10.3934/dcds.2010.27.265

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, Japan

Received  April 2009 Revised  October 2009 Published  February 2010

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.
Keywords: Julia set, Turing model, Trapping region., Escape to infinity, Lattice dynamical system.
Mathematics Subject Classification: Primary: 37N25, 37N10; Secondary: 35K5.
Citation: Hunseok Kang. Asymptotic behavior of a discrete turing model. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 265-284. doi: 10.3934/dcds.2010.27.265
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