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Stable Bifurcations in Multi-species Semelparous Population Models

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Advances in Difference Equations and Discrete Dynamical Systems (ICDEA 2016)

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Abstract

It is known that the behavior of a nonlinear semelparous Leslie matrix model with the basic reproduction number close to one can be approximated by a solution of a Lotka-Volterra differential equation. Furthermore, even in multi-species cases, a similar approximation works as long as every species is semelparous. This paper gives a mathematical basis to this approximation and shows that Lotka-Volterra equations are helpful to study a certain bifurcation problem of multi-species semelparous population models. With the help of this approximation method, we find an example of coexistence of two biennial populations with temporal segregation. This example provides a new mechanism of producing population cycles.

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Acknowledgments

This work was supported by KAKENHI Grant Number JP16K05279.

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Authors and Affiliations

  1. Faculty of Engineering, University of Miyazaki, Gakuen Kibanadai Nishi 1-1, Miyazaki, 889-2192, Japan

    Ryusuke Kon

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  1. Ryusuke Kon
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Correspondence to Ryusuke Kon .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, Texas, USA

    Saber Elaydi

  2. Department of Information Science, Okayama University of Science, Okayama, Japan

    Yoshihiro Hamaya

  3. Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka, Japan

    Hideaki Matsunaga

  4. Institut für Mathematik, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

    Christian Pötzsche

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Kon, R. (2017). Stable Bifurcations in Multi-species Semelparous Population Models. In: Elaydi, S., Hamaya, Y., Matsunaga, H., Pötzsche, C. (eds) Advances in Difference Equations and Discrete Dynamical Systems. ICDEA 2016. Springer Proceedings in Mathematics & Statistics, vol 212. Springer, Singapore. https://doi.org/10.1007/978-981-10-6409-8_1

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