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Study of a Mixed Dispersal Population Dynamics Model

  • Marina Chugunova
  • Baasansuren Jadamba
  • Chiu-Yen KaoEmail author
  • Christine Klymko
  • Evelyn Thomas
  • Bingyu Zhao
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (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.

Notes

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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Marina Chugunova
    • 1
  • Baasansuren Jadamba
    • 2
  • Chiu-Yen Kao
    • 3
    Email author
  • Christine Klymko
    • 4
  • Evelyn Thomas
    • 5
  • Bingyu Zhao
    • 6
  1. 1.Department of MathematicsClaremont Graduate UniversityClaremontUSA
  2. 2.School of Mathematical SciencesRochester Institute of TechnologyRochesterUSA
  3. 3.Department of Mathematical SciencesClaremont McKenna CollegeClaremontUSA
  4. 4.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  5. 5.Department of Mathematics and StatisticsUniversity of Maryland Baltimore CountyBaltimoreUSA
  6. 6.Department of Applied MathematicsBrown UniversityProvidenceUSA

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