Abstract：
This paper reports an important conclusion that self-diffusion is not a necessary condition for inducing Turing patterns, while taxis could establish complex pattern phenomena. We investigate pattern formation in a zooplankton-phytoplankton model incorporating phytoplankton-taxis, where phytoplankton-taxis describes the zooplankton that tends to move toward the high-densities region of the phytoplankton population. By using the phytoplankton-taxis sensitivity coefficient as the Turing instability threshold, one shows that the model exhibits Turing instability only when repulsive phytoplankton-taxis is added into the system, while the attractive-type phytoplankton-taxis cannot induce Turing instability of the system. In addition, the system does not exhibit Turing instability when the phytoplankton-taxis disappears. Numerically, we display the complex patterns in 1D, 2D domains and on spherical and zebra surfaces, respectively. In summary, our results indicate that the phytoplankton-taxis plays a pivotal role in giving rise to the Turing pattern formation of the model. Additionally, these theoretical and numerical results contribute to our understanding of the complex interaction dynamics between zooplankton and phytoplankton populations.
摘要：
本文报道了一个重要的结论，即自扩散不是诱导图灵模式的必要条件，而出租车可以建立复杂的模式现象。我们研究了结合浮游植物-出租车的浮游动物-浮游植物模型中的模式形成，其中浮游植物-出租车描述了倾向于向浮游植物种群的高密度区域移动的浮游动物。通过使用浮游植物-滑行敏感系数作为图灵不稳定性阈值，一个表明，只有当排斥性浮游植物-出租车被添加到系统中时，模型才表现出图灵不稳定性，而有吸引力的浮游植物-出租车不能诱导系统的图灵不稳定性。此外,当浮游植物出租车消失时，系统不会表现出图灵不稳定性。数字上,我们在1D中显示复杂的模式，2D域以及球形和斑马表面，分别。总之,我们的结果表明，浮游植物-出租车在导致模型的图灵模式形成中起着关键作用。此外,这些理论和数值结果有助于我们理解浮游动物和浮游植物种群之间复杂的相互作用动力学。
