SPATIO-TEMPORAL COEXISTENCE IN THE CROSS-DIFFUSION COMPETITION SYSTEM

HIROFUMI IZUHARA; SHUNSUKE KOBAYASHI

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SPATIO-TEMPORAL COEXISTENCE IN THE CROSS-DIFFUSION COMPETITION SYSTEM

机译：交叉扩散竞争系统中的时空共存

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We study a two component cross-diffusion competition systemwhich describes the population dynamics between two biological species. Sincethe cross-diffusion competition system possesses the so-called population pressureeffects, a variety of solution behaviors can be exhibited compared withthe classical diffusion competition system. In particular, we discuss on the existenceof spatially non-constant time periodic solutions. Applying the centermanifold theory and the standard normal form theory, the cross-diffusion competitionsystem is reduced to a two dimensional dynamical system around adoubly degenerate point. As a result, we show the existence of stable time periodicsolutions in the system. This means spatio-temporal coexistence betweentwo biological species.

机译：我们研究了两个组件交叉扩散竞争系统这描述了两种生物物种之间的人口动态。自从交叉扩散竞争系统具有所谓的人口压力效果，可以展现各种解决方案行为古典扩散竞争体系。特别是，我们讨论存在空间非恒定时间定期解决方案。应用中心歧管理论与标准正常形式理论，交叉扩散竞争系统减少到周围的二维动力系统双重退化点。结果，我们展示了稳定时间的存在系统中的解决方案。这意味着两种之间的时空共存两个生物物种。

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来源
《Discrete and Continuous Dynamical Systems,Series S》 |2021年第3期|919-933|共15页
作者
HIROFUMI IZUHARA; SHUNSUKE KOBAYASHI;
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作者单位

Faculty of Engineering University of Miyazaki1-1 Gakuen Kibanadainishi Miyazaki 889-2192 Japan;

Graduate School of Science and Technology Meiji UniversityKanagawa 214-8571 Japan;

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正文语种 eng
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Periodic solution; cross-diffusion; center manifold theory; spatial segregation;

机译：定期解决方案;交叉扩散;中心歧管理论;空间隔离;

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SPATIO-TEMPORAL COEXISTENCE IN THE CROSS-DIFFUSION COMPETITION SYSTEM

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