（2+1）维趋化模型的时空演化
Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model
摘要：
对一类具有Logistic增长项的（2+1）维Keller-Segel（KS）型趋化性模型的非线性动力学进行了模拟研究.由于KS模型能够显示自聚集现象，因此被广泛用于模拟许多生物系统中的自组织现象。我们表明，相应的动力学可能会导致一个稳定的状态，在有限的时间内发散，以及时空不规则图案的形成。后者，特别是，似乎是混沌的有界的解决方案的范围内的一部分，所示的小波功率谱分析。在趋化系数$(χ)$的值足够大和/或生长速率$r$低于临界值$r_c$的情况下实现稳态。对于$r > r_c$，模型微分方程的解在有限时间内发散。我们还报告了不同值的$χ$，$r$和扩散系数$D$的斑图形成制度。
英文摘要：
Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller-Segel (KS) type with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to a steady-state, divergence in a finite time as well as the formation of spatiotemporal irregular patterns. The latter, in particular, appear to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady states are achieved with sufficiently large values of the chemotactic coefficient $(χ)$ and/or with growth rates $r$ below a critical value $r_c$. For $r > r_c$, the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime for different values of $χ$, $r$ and the diffusion coefficient $D$.
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