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Study of a Mixed Dispersal Population Dynamics Model

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Topics in Numerical Partial Differential Equations and Scientific Computing

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 160))

Abstract

In this paper, we consider a mixed dispersal model with periodic and Dirichlet boundary conditions and its corresponding linear eigenvalue problem. This model describes the time evolution of a population which disperses both locally and nonlocally. We investigate how long time dynamics depend on the parameter values. Furthermore, we study the minimization of the principal eigenvalue under the constraints that the resource function is bounded from above and below, and with a fixed total integral. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for the species to die out more slowly or survive more easily. Our numerical simulations indicate that the optimal favorable region tends to be a simply connected domain. Numerous results are shown to demonstrate various scenarios of optimal favorable regions for periodic and Dirichlet boundary conditions.

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Acknowledgments

The authors would like to thank Institute for Mathematics and its Applications at University of Minnesota for hosting a special workshop on “WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing.” This paper summarized the project results of Team3 on principal eigenvalue for a population dynamics model problem with both local and nonlocal dispersal.

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Authors and Affiliations

  1. Department of Mathematics, Claremont Graduate University, Claremont, CA, 91711, USA

    Marina Chugunova

  2. School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, 14623, USA

    Baasansuren Jadamba

  3. Department of Mathematical Sciences, Claremont McKenna College, Claremont, CA, 91711, USA

    Chiu-Yen Kao

  4. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA

    Christine Klymko

  5. Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD, 21250, USA

    Evelyn Thomas

  6. Department of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Bingyu Zhao

Authors
  1. Marina Chugunova
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  2. Baasansuren Jadamba
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  3. Chiu-Yen Kao
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  4. Christine Klymko
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  5. Evelyn Thomas
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  6. Bingyu Zhao
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Corresponding author

Correspondence to Chiu-Yen Kao .

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Editors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisana State University, Baton Rouge, Louisiana, USA

    Susanne C. Brenner

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Chugunova, M., Jadamba, B., Kao, CY., Klymko, C., Thomas, E., Zhao, B. (2016). Study of a Mixed Dispersal Population Dynamics Model. In: Brenner, S. (eds) Topics in Numerical Partial Differential Equations and Scientific Computing. The IMA Volumes in Mathematics and its Applications, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6399-7_3

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