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Mathematics for Ecology and Environmental Sciences pp 51–80Cite as

The Effects of Migration on Persistence and Extinction

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Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Summary

The interrelationship between organisms and the environment is essential to the stability or permanence of an ecological system, and the effect of migration on the possibility of species coexistence in an ecological community has been an important subject of research in population biology. Numerous types of models have been proposed and have been used to describe movement or dispersal of population individuals among patches. Some of the existing models deal with a single population dispersing among patches and others deal with predator-prey and competition interactions in patchy environments. Most previous models are based on autonomous ordinary differential equations. Recently, some authors have also studied the influence of migration on time-dependent population models.

In this chapter, we attempt to review key related research and introduce a set of new results for time-dependent population models in patchy environments. We consider a single-species model described by a set of autonomous ordinary differential equations or non-autonomous equations with periodic functions or with dispersal time delays. Also, we consider an age-structure model with or without dispersal delays. Further, we discuss predator-prey or competitive models described by autonomous or time-dependent ordinary differential equations.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University Nanjing, 210097, China

    Jingan Cui

  2. Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Japan

    Yasuhiro Takeuchi

Authors
  1. Jingan Cui
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  2. Yasuhiro Takeuchi
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Editors and Affiliations

  1. Faculty of Engineering Department of Systems Engineering, Shizuoka University, Hamamatsu 3-5-1, 432-8561, Shizuoka, Japan

    Yasuhiro Takeuchi  & Kazunori Sato  & 

  2. Department of Biology, Kyushu University, 812-8581, Fukuoka, Japan

    Yoh Iwasa

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Cui, J., Takeuchi, Y. (2007). The Effects of Migration on Persistence and Extinction. In: Takeuchi, Y., Iwasa, Y., Sato, K. (eds) Mathematics for Ecology and Environmental Sciences. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34428-5_4

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