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 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 simplyconnected 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):
 LLNLJRNL674461
Journal ID: ISSN 09406573
 Grant/Contract Number:
 AC5207NA27344
 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 09406573
 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:10.1007/9781493963997_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:10.1007/9781493963997_3.
Chugunova, Marina, Jadamba, Baasansuren, Kao, Chiu Yen, Klymko, Christine F., Thomas, Evelyn, and Zhao, Bingyu. 2016.
"Study of a mixed dispersal population dynamics model". United States.
doi:10.1007/9781493963997_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 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 simplyconnected domain. Numerous results are shown to demonstrate various scenarios of optimal favorable regions for periodic and Dirichlet boundary conditions.},
doi = {10.1007/9781493963997_3},
journal = {The IMA Volumes in Mathematics and its Applications},
number = ,
volume = 160,
place = {United States},
year = 2016,
month = 8
}

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