國立高雄大學圖資館 |

Traveling Waves in Cyclic Ecological Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Traveling Waves in Cyclic Ecological Systems.
作者:	Wang, Zihao.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, 2023
面頁冊數:	195 p.
附註:	Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
附註:	Advisor: Volpert, Vladimir;Bayliss, Alvin.
Contained By:	Dissertations Abstracts International85-06B.
標題:	Applied mathematics.
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30696499
ISBN:	9798381175431

Traveling Waves in Cyclic Ecological Systems.
Wang, Zihao.

Traveling Waves in Cyclic Ecological Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 195 p.

Source: Dissertations Abstracts International, Volume: 85-06, Section: B.

Thesis (Ph.D.)--Northwestern University, 2023.

This item must not be sold to any third party vendors.

This dissertation is concerned with mathematical models for how different species (of animals, plants, bacteria, or other diffusion things) spread out and compete with one another. It examines the dynamics of traveling wave solutions within multi-species cyclic ecological systems. We develop, analyze and simulate deterministic models mainly for two and four-species ecosystems, which are described by systems of reaction-diffusion partial differential equations. These models account for species mobility via Fickian diffusion and inter-species interactions based on a cyclic competition scheme. The study incorporates analytical methods, specifically asymptotic and perturbative approaches, alongside numerical simulations, to investigate in detail the inter-species competition dynamics, traveling wave propagation phenomena, and the determination of dominant species or equilibrium states. In the context of species invasions, we show that direct inter-species competition, mobility, and birthrates, as well as their interrelationships with one another, are the factors that determine the dominant species and long-term dynamics of cyclic systems. These key factors are expressed by specific parameters within the deterministic systems, and asymptotic solutions are presented across various limiting parameter regimes, which are further substantiated by numerical simulations.We initially examine traveling wave solutions of the Lotka-Volterra competition-diffusion system for two species in the bistable region. This includes an investigation into the propagation speed of traveling waves and, most importantly, the sign of the speed, which determines the winner of the competition, in several limiting cases. These cases are categorized into (i) strong competition, where inter-species competition for each species notably surpasses intra-species competition, and (ii) moderate competition, where inter-and intra-species competitions are of similar strength. Furthermore, scenarios involving fast and slow competitors—defined by significantly different diffusion coefficients—are analyzed.Building upon the Lotka-Volterra two-species competition model, we study a four-species cyclic community. Our research reveals intriguing dynamics in the four-species cyclic ecosystem. We observe the formation of two stable alliances between non-competing species in the parameter regimes where inter-species competition exceeds intra-species competition. We derive conditions under which one alliance can displace the other in an “ invasion ” scenario. In particular, we examine the situation where both alliances are evenly matched — a state referred to as the “ standstill problem. ” Our investigation focuses on three specific parameter regimes: (i) moderate competition, (ii) strong competition, and (iii) slow competitors (diffusivities for one alliance are asymptotically close to zero, or, alternatively, birthrates for one alliance are asymptotically large). Analytical results obtained from this section are cross-verified with numerical computations and previous findings related to the two-species model, demonstrating a high degree of agreement. Lastly, we collect the accumulated research findings and introduce two new methodologies: piecewise linear approximation and front propagation analysis. The former method, which involves linearizing the system in different spatial regions and subsequently matching to estimate the propagation speed, encountered challenges. Specifically, the piecewise linear method was not entirely effective for the traveling wave problems. The differences between the approximate solutions and the numerical simulations were likely attributable to the complexity of the interspecies interface. Direct derivative matching in this region seems to neglect many vital details, leading to a solution that lacks sufficient accuracy. However, this method was not without value. Despite its limitations, it provided instructive insights that inspired us to reconsider our approach. Drawing from these preliminary findings, we developed alternative methodologies, as detailed in Chapters 2 and 3. On the other hand, the front propagation analysis method offers an estimation technique for propagation speeds of unstable states in the presence of pulled fronts. Propagation speeds are computed and estimated in several asymptotic limit cases. For four-species systems, the interface between the advancing and retreating states is intricate, and intermediate buffer states can emerge under specific parameter regimes. When this happens, pulled fronts appear, and this method proves effective in estimating the propagation speed between states.

ISBN: 9798381175431Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Front propagation analysis

Traveling Waves in Cyclic Ecological Systems.
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100 1 $a Wang, Zihao. $0 (orcid)0000-0002-8781-4597 $3 967022
245 1 0 $a Traveling Waves in Cyclic Ecological Systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 195 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
500 $a Advisor: Volpert, Vladimir;Bayliss, Alvin.
502 $a Thesis (Ph.D.)--Northwestern University, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a This dissertation is concerned with mathematical models for how different species (of animals, plants, bacteria, or other diffusion things) spread out and compete with one another. It examines the dynamics of traveling wave solutions within multi-species cyclic ecological systems. We develop, analyze and simulate deterministic models mainly for two and four-species ecosystems, which are described by systems of reaction-diffusion partial differential equations. These models account for species mobility via Fickian diffusion and inter-species interactions based on a cyclic competition scheme. The study incorporates analytical methods, specifically asymptotic and perturbative approaches, alongside numerical simulations, to investigate in detail the inter-species competition dynamics, traveling wave propagation phenomena, and the determination of dominant species or equilibrium states. In the context of species invasions, we show that direct inter-species competition, mobility, and birthrates, as well as their interrelationships with one another, are the factors that determine the dominant species and long-term dynamics of cyclic systems. These key factors are expressed by specific parameters within the deterministic systems, and asymptotic solutions are presented across various limiting parameter regimes, which are further substantiated by numerical simulations.We initially examine traveling wave solutions of the Lotka-Volterra competition-diffusion system for two species in the bistable region. This includes an investigation into the propagation speed of traveling waves and, most importantly, the sign of the speed, which determines the winner of the competition, in several limiting cases. These cases are categorized into (i) strong competition, where inter-species competition for each species notably surpasses intra-species competition, and (ii) moderate competition, where inter-and intra-species competitions are of similar strength. Furthermore, scenarios involving fast and slow competitors—defined by significantly different diffusion coefficients—are analyzed.Building upon the Lotka-Volterra two-species competition model, we study a four-species cyclic community. Our research reveals intriguing dynamics in the four-species cyclic ecosystem. We observe the formation of two stable alliances between non-competing species in the parameter regimes where inter-species competition exceeds intra-species competition. We derive conditions under which one alliance can displace the other in an “ invasion ” scenario. In particular, we examine the situation where both alliances are evenly matched — a state referred to as the “ standstill problem. ” Our investigation focuses on three specific parameter regimes: (i) moderate competition, (ii) strong competition, and (iii) slow competitors (diffusivities for one alliance are asymptotically close to zero, or, alternatively, birthrates for one alliance are asymptotically large). Analytical results obtained from this section are cross-verified with numerical computations and previous findings related to the two-species model, demonstrating a high degree of agreement. Lastly, we collect the accumulated research findings and introduce two new methodologies: piecewise linear approximation and front propagation analysis. The former method, which involves linearizing the system in different spatial regions and subsequently matching to estimate the propagation speed, encountered challenges. Specifically, the piecewise linear method was not entirely effective for the traveling wave problems. The differences between the approximate solutions and the numerical simulations were likely attributable to the complexity of the interspecies interface. Direct derivative matching in this region seems to neglect many vital details, leading to a solution that lacks sufficient accuracy. However, this method was not without value. Despite its limitations, it provided instructive insights that inspired us to reconsider our approach. Drawing from these preliminary findings, we developed alternative methodologies, as detailed in Chapters 2 and 3. On the other hand, the front propagation analysis method offers an estimation technique for propagation speeds of unstable states in the presence of pulled fronts. Propagation speeds are computed and estimated in several asymptotic limit cases. For four-species systems, the interface between the advancing and retreating states is intricate, and intermediate buffer states can emerge under specific parameter regimes. When this happens, pulled fronts appear, and this method proves effective in estimating the propagation speed between states.
590 $a School code: 0163.
650 4 $a Applied mathematics. $3 377601
650 4 $a Ecology. $3 180214
650 4 $a Systematic biology. $3 708586
653 $a Front propagation analysis
653 $a Inter-species interactions
653 $a Instructive insights
653 $a Propagation speeds
653 $a Four-species systems
690 $a 0364
690 $a 0423
690 $a 0329
710 2 $a Northwestern University. $b Engineering Sciences and Applied Mathematics. $3 886704
773 0 $t Dissertations Abstracts International $g 85-06B.
790 $a 0163
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30696499