Nonconstant positive steady states and pattern formation of 1D prey-taxis systems
Nonconstant positive steady states and pattern formation of 1D prey-taxis systems
复制标题
一维猎物趋行系统的非恒定正稳态和模式形成
DOI：
10.1007/s00332-016-9326-5
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
SHAO LINJIE
中科院分区：
文献类型：
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作者：
WANG QI;SONG YANG;SHAO LINJIE
猎物趋向是捕食者优先向猎物密度最高的区域移动的过程。众所周知，它在生物控制和维持生物多样性方面具有重要作用。为了模拟捕食者和猎物物种的共存和空间分布，本文关注一维域上具有一般功能响应的多种猎物趋向系统的非恒定正稳态。分析正平衡的线性稳定性，表明当存在猎物排斥（例如，由于捕食者物种中的体积填充效应或猎物物种中的群体防御）时，猎物趋向性会破坏猎物-捕食者同质性，否则猎物趋向性会稳定同质性。然后，我们通过严格的分岔分析来研究系统非恒定正稳态的存在性和稳定性。此外，我们提供详细而彻底的计算来确定局部分支的干草叉和转动方向等属性。我们的稳定性结果还为反应-平流-扩散系统（包括本文中考虑的猎物趋向模型）提供了稳定的波模式选择机制。最后，我们利用霍林-坦纳动力学提供了猎物趋向系统的数值研究，以说明和支持我们的理论发现。我们的数值模拟表明，2×2 猎物趋向系统能够模拟各种引人注目模式的形成和演化，例如尖峰、周期性振荡和粗化，即使域是一维的也是如此。这些动力学可以模拟相互作用的猎物和捕食者物种的共存和空间分布。我们还对系统参数如何影响这些模型中的模式形成提供了一些见解。
Prey-taxis is the process that predators move preferentially toward patches with highest density of prey. It is well known to have an important role in biological control and the maintenance of biodiversity. To model the coexistence and spatial distributions of predator and prey species, this paper concerns nonconstant positive steady states of a wide class of prey-taxis systems with general functional responses over 1D domain. Linearized stability of the positive equilibrium is analyzed to show that prey-taxis destabilizes prey–predator homogeneity when prey repulsion (e.g., due to volume-filling effect in predator species or group defense in prey species) is present, and prey-taxis stabilizes the homogeneity otherwise. Then, we investigate the existence and stability of nonconstant positive steady states to the system through rigorous bifurcation analysis. Moreover, we provide detailed and thorough calculations to determine properties such as pitchfork and turning direction of the local branches. Our stability results also provide a stable wave mode selection mechanism for thee reaction–advection–diffusion systems including prey-taxis models considered in this paper. Finally, we provide numerical studies of prey-taxis systems with Holling–Tanner kinetics to illustrate and support our theoretical findings. Our numerical simulations demonstrate that the 2×2 prey-taxis system is able to model the formation and evolution of various striking patterns, such as spikes, periodic oscillations, and coarsening even when the domain is one-dimensional. These dynamics can model the coexistence and spatial distributions of interacting prey and predator species. We also give some insights on how system parameters influence pattern formation in these models.