Turing instability and wave patterns for a symmetric discrete competitive Lotka-Volterra system
Turing instability and wave patterns for a symmetric discrete competitive Lotka-Volterra system
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发表时间：
2011-05
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通讯作者：
Yutao Han;B. Han;Lu Zhang;Li Xu;Mei-Feng Li;Guang Zhang
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作者：
Yutao Han;B. Han;Lu Zhang;Li Xu;Mei-Feng Li;Guang Zhang
研究了一类对称离散竞争Lotka-Volterra系统的图灵不稳定性问题。为此，得到了一般离散系统产生图灵不稳定性的条件，并将这一结论应用于离散竞争Lotka-Volterra系统。然后对不同参数下的离散模型进行了一系列数值模拟。结果表明，离散竞争Lotka-Volterra系统可以在图灵不稳定区域产生多种波形。特别是扩散系数可以等效，即既不存在“活化剂”，也不存在“抑制剂”。对于相应的连续模型则不能得到类似的结果。另一方面，通过计算说明了特征值的数量，可以清晰地表达不稳定空间。从而也解释了图灵机制。
In this paper, Turing instability of a symmetric discrete competitive Lotka-Volterra system is considered. To this end, conditions for producing Turing instability of a general discrete system is attained and this conclusion is applied to the discrete competition Lotka-Volterra system. Then a series of numerical simulations of the discrete model are performed with different parameters. Results show that the discrete competitive Lotka-Volterra system can generate a large variety of wave patterns in the Turing instability region. Particularly, the diffusion coefficients can be equivalent, that is, there is neither "activator" nor "inhibitor". Similar results can not be obtained for the corresponding continuous models. On the other hand, the number of the eigenvalues is illuminated by calculation and the unstable spaces can be clearly expressed. Thus, the Turing mechanism is also explained.