Global attractor and Lyapunov function for one-dimensional Deneubourg chemotaxis system
Global attractor and Lyapunov function for one-dimensional Deneubourg chemotaxis system
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DOI：
10.32917/hmj/1564106547
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发表时间：
2019-07
影响因子：
0.2
通讯作者：
Kanako Noda;Koichi Osaki
中科院分区：
文献类型：
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作者：
Kanako Noda;Koichi Osaki
摘要。我们研究了Deneubourg （intes Sociaux 24(1977)）提出的一维趋化系统解的全局时间存在性和渐近行为。该系统模拟了群居昆虫的自组织筑巢过程。当时间尺度趋近于0时，Deneubourg模型退化为线性退化的抛物-抛物型Keller-Segel系统。我们首先证明了解的全局时间存在性。然后定义解的动力系统，构造全局吸引子。此外，在假设工虫的静息率很大的情况下，构造了唯一齐次均衡的Lyapunov泛函，表明全局吸引子仅由均衡组成。
A bstract . We study the global-in-time existence and the asymptotic behavior of solutions to a one-dimensional chemotaxis system presented by Deneubourg (Insectes Sociaux 24 (1977)). The system models the self-organized nest construction process of social insects. In the limit as a time-scale coe‰cient tends to 0, the Deneubourg model reduces to a parabolic-parabolic Keller-Segel system with linear degradation. We first show the global-in-time existence of solutions. We next define the dynamical system of solutions and construct the global attractor. In addition, under the assumption of a large resting rate of worker insects, we construct a Lyapunov functional for the unique homogeneous equilibrium, which indicates that the global attractor consists only of the equilibrium.