论文标题
反应-Cattaneo系统中紧急行进波的非线性动力学
Nonlinear dynamics of emergent traveling waves in a reaction-Cattaneo system
论文作者
论文摘要
标准扩散方程基于分散物种的布朗运动，而无需考虑个体运动的持久性。此描述允许在其原始位置预测无限速度的任意距离上瞬时扩散。此功能是不现实的，尤其是考虑生物学入侵动态，并且更好的描述需要考虑惯性分散。我们在这里研究了非触发扰动对一维反应 - 塔奈系统稳态的行为，该系统具有描述种群动力学或火焰传播模型的立方多项式术语。据分析表明，尽管线性分析预测均匀状态的稳定性，但对非线性贡献的考虑导致时空扰动作为行驶波的增长。我们表明，扩散通量的有限松弛时间的存在会改变行动波的速度。具体而言，我们发现波速随着磁通量的有限松弛时间的增加而衰减。我们的分析预测通过数值结果很好地证实了。
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an arbitrarily large distances from their original location predicting infinite velocities. This feature is unrealistic particularly while considering biological invasion dynamics and a better description needs the consideration of dispersal with inertia. We here examine the behavior of non-infinitesimal perturbation on the steady state of an one-dimensional reaction-Cattaneo system with a cubic polynomial source term describing population dynamics or flame propagation models. It has been shown analytically that while linear analysis predicts stability of the homogeneous state, consideration of nonlinear contribution leads to a growth of spatiotemporal perturbation as a traveling wave. We show that the presence of a small finite relaxation time of the diffusive flux modifies the speed of the traveling wave. Specifically, we find that the wave speed decays with an increase of a finite relaxation time of flux. Our analytical predictions are well corroborated with the numerical results.
