网络上单种群反应扩散模型的时滞诱导类Turing-like波
Delay induced Turing-like waves for one species reaction-diffusion model on a network
摘要：
研究了一类定义在复杂网络上的单种群时滞反应扩散系统。行波被预测发生如下对称破缺不稳定性的均匀稳定的解决方案，受到外部非均匀扰动。这些都是广义图灵类波，在一个单一的物种种群动力学模型中实现，作为意外的副产品，在扩散部分的延迟。通过对时滞微分方程进行线性稳定性分析，在数学上给出了不稳定性发生的充分条件。这里开发的方法利用了Lambert W函数的性质。理论的预测证实了直接数值模拟进行的经典Fisher模型的修改版本，定义在Watts-Strogatz网络，并列入延迟。
英文摘要：
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay.
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