# Study of a mixed dispersal population dynamics model

## Abstract

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.

- Authors:

- Claremont Graduate Univ., Claremont, CA (United States). Dept. of Mathematics
- Rochester Institute of Technology, Rochester, NY (United States). School of Mathematics Sciences
- Claremont McKenna College, Claremont, CA (United States). Dept. of Mathematical Sciences
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States). Dept. of Mathematics and Statistics
- Brown Univ., Providence, RI (United States). Dept. of Applied Mathematics

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1305855

- Report Number(s):
- LLNL-JRNL-674461

Journal ID: ISSN 0940-6573

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- The IMA Volumes in Mathematics and its Applications

- Additional Journal Information:
- Journal Volume: 160; Journal ID: ISSN 0940-6573

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

### Citation Formats

```
Chugunova, Marina, Jadamba, Baasansuren, Kao, Chiu -Yen, Klymko, Christine F., Thomas, Evelyn, and Zhao, Bingyu.
```*Study of a mixed dispersal population dynamics model*. United States: N. p., 2016.
Web. doi:10.1007/978-1-4939-6399-7_3.

```
Chugunova, Marina, Jadamba, Baasansuren, Kao, Chiu -Yen, Klymko, Christine F., Thomas, Evelyn, & Zhao, Bingyu.
```*Study of a mixed dispersal population dynamics model*. United States. doi:10.1007/978-1-4939-6399-7_3.

```
Chugunova, Marina, Jadamba, Baasansuren, Kao, Chiu -Yen, Klymko, Christine F., Thomas, Evelyn, and Zhao, Bingyu. Sat .
"Study of a mixed dispersal population dynamics model". United States.
doi:10.1007/978-1-4939-6399-7_3. https://www.osti.gov/servlets/purl/1305855.
```

```
@article{osti_1305855,
```

title = {Study of a mixed dispersal population dynamics model},

author = {Chugunova, Marina and Jadamba, Baasansuren and Kao, Chiu -Yen and Klymko, Christine F. and Thomas, Evelyn and Zhao, Bingyu},

abstractNote = {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.},

doi = {10.1007/978-1-4939-6399-7_3},

journal = {The IMA Volumes in Mathematics and its Applications},

number = ,

volume = 160,

place = {United States},

year = {Sat Aug 27 00:00:00 EDT 2016},

month = {Sat Aug 27 00:00:00 EDT 2016}

}