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Title: Study of a mixed dispersal population dynamics model

Journal Article · · The IMA Volumes in Mathematics and its Applications
 [1];  [2];  [3];  [4];  [5];  [6]
  1. Claremont Graduate Univ., Claremont, CA (United States). Dept. of Mathematics
  2. Rochester Institute of Technology, Rochester, NY (United States). School of Mathematics Sciences
  3. Claremont McKenna College, Claremont, CA (United States). Dept. of Mathematical Sciences
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  5. Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States). Dept. of Mathematics and Statistics
  6. Brown Univ., Providence, RI (United States). Dept. of Applied Mathematics
+ Show Author Affiliations

In this study, 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 non-locally. 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.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1305855
Report Number(s):
LLNL-JRNL-674461
Journal Information:
The IMA Volumes in Mathematics and its Applications, Vol. 160; ISSN 0940-6573
Country of Publication:
United States
Language:
English

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97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE