Spatio-temporal coexistence in the cross-diffusion competition system
Spatio-temporal coexistence in the cross-diffusion competition system
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DOI：
10.3934/dcdss.2020228
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
H. Izuhara;Shunsuke Kobayashi
中科院分区：
文献类型：
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作者：
H. Izuhara;Shunsuke Kobayashi
我们研究了一个描述两个生物物种间种群动态的双组分交叉扩散竞争系统。由于交叉扩散竞争系统具有所谓的种群压力效应，因此与经典扩散竞争系统相比，交叉扩散竞争系统可以表现出多种解决行为。特别地，我们讨论了空间非常时间周期解的存在性。应用中心流形理论和标准范式理论，将交叉扩散竞争系统简化为围绕一个双简并点的二维动力系统。结果证明了系统存在稳定的时间周期解。这意味着两个生物物种之间的时空共存。
We study a two component cross-diffusion competition system which describes the population dynamics between two biological species. Since the cross-diffusion competition system possesses the so-called population pressure effects, a variety of solution behaviors can be exhibited compared with the classical diffusion competition system. In particular, we discuss on the existence of spatially non-constant time periodic solutions. Applying the center manifold theory and the standard normal form theory, the cross-diffusion competition system is reduced to a two dimensional dynamical system around a doubly degenerate point. As a result, we show the existence of stable time periodic solutions in the system. This means spatio-temporal coexistence between two biological species.