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computational study of traveling wave solutions and global stability of predator-prey models

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Date Issued:
2016
Abstract/Description:
In this thesis, we study two types of reaction-diffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will bestudied. The first is autocatalytic chemical reaction of order $m$ without decay. The second is chemical reaction of order $m$ with a decay of order $l$, where $m$ and $l$ are positive integers and $m(>)l\ge1$. A typical system is $A + 2B \rightarrow3B$ and $B\rightarrow C$ involving three chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.We use numerical computation to give more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves. For autocatalytic reaction of order $m = 2$ with linear decay $l = 1$, which hasa particular important role in biological pattern formation, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.The second part of this thesis is on the global stability of diffusive predator-prey system of Leslie Type and Holling-Tanner Type in a bounded domain $\Omega\subset R^N$ with no-flux boundary condition. By using a new approach, we establish much improved global asymptotic stability of a unique positiveequilibrium solution. We also show the result can be extended to more general type of systems with heterogeneous environment and/or other kind of kinetic terms.
Title: computational study of traveling wave solutions and global stability of predator-prey models.
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Name(s): Zhu, Yi, Author
Qi, Yuanwei, Committee Chair
Rollins, David, Committee Member
Shuai, Zhisheng, Committee Member
Zhai, Lei, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2016
Publisher: University of Central Florida
Language(s): English
Abstract/Description: In this thesis, we study two types of reaction-diffusion systems which have direct applications in understanding wide range of phenomena in chemical reaction, biological pattern formation and theoretical ecology.The first part of this thesis is on propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will bestudied. The first is autocatalytic chemical reaction of order $m$ without decay. The second is chemical reaction of order $m$ with a decay of order $l$, where $m$ and $l$ are positive integers and $m(>)l\ge1$. A typical system is $A + 2B \rightarrow3B$ and $B\rightarrow C$ involving three chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.We use numerical computation to give more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves. For autocatalytic reaction of order $m = 2$ with linear decay $l = 1$, which hasa particular important role in biological pattern formation, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.The second part of this thesis is on the global stability of diffusive predator-prey system of Leslie Type and Holling-Tanner Type in a bounded domain $\Omega\subset R^N$ with no-flux boundary condition. By using a new approach, we establish much improved global asymptotic stability of a unique positiveequilibrium solution. We also show the result can be extended to more general type of systems with heterogeneous environment and/or other kind of kinetic terms.
Identifier: CFE0006519 (IID), ucf:51359 (fedora)
Note(s): 2016-12-01
Ph.D.
Sciences, Mathematics
Doctoral
This record was generated from author submitted information.
Subject(s): isothermal chemical systems -- multiple peak solutions -- minimum speed -- existence -- non-existence -- traveling wave -- global asymptotic stability -- positive equilibrium solution -- comparison principle -- diffusive predator-prey systems
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0006519
Restrictions on Access: public 2016-12-15
Host Institution: UCF

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