Mathematical modelling of predator-prey dynamics in complex environments
Başlık çevirisi mevcut değil.
- Tez No: 539853
- Danışmanlar: Dr. ANDREW MOROZOV
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2017
- Dil: İngilizce
- Üniversite: University of Leicester
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 165
Özet
Özet yok.
Özet (Çeviri)
The main aim of mathematical ecology is to explore interactions among organisms and the environment where they live, and predator-prey interaction is one of the major type of interactions observed in nature. Models of predator-prey systems - mathematically described by ODEs, PDEs or integro-differential equations - have a long and illustrious history starting from the seminal works by Lotka and Volterra. However, despite a large number of existing publications in the literature, some fundamental questions related to this type of systems still remain open. For example, the spatial heterogeneity of the environment and its role in stabilisation of predator-prey dynamics and persistence of species is still not well understood. Another major challenge is the effect of external forcing (e.g. daily, seasonal, or other variation of model parameters) on long-term dynamics of the predatorprey or host parasite models. Finally, the parameterisation of model functions describing species interactions, for instance, formulation of the functional response of predator, can play a crucial role in the model outcomes. In the present dissertation, we explore the three above challenging issues (i.e. space heterogeneity, external forcing and model parametrisation) on the patterns of spatio-temporal dynamics of predator-prey or/and host-parasite systems and their stability. In particular, we revisit the famous paradox of enrichment which is classical in mathematical biology and explain how the spatial heterogeneity and animal movement on various time scales can stabilise the system characterised by an infinitely large carrying capacity (Chapter 2). Mathematically, we use a i system of integro-differential equations and consider a tri-trophic planktonic system as a case study. In the two next chapters, we consider the role of daily and seasonal variation of temperature on the control of pathogenic bacteria by their predators: bacteriophages (i.e. bacterial viruses). As an important ecological case study, we explore seasonable dynamics of the infectious bacteria causing the lethal disease Melioidosis in Thailand. In the beginning we model interaction in the top water of a rice field (Chapter 3). Here we build two different models of hostparasite interactions based on ODEs and DDEs (delay differential equations). In Chapter 4, by using reaction-diffusion framework, we extend the previous model of bacteria-phage interactions to consider bacteria-phage dynamics in soil. Using our modelling approach we can make predictions about disease management of Melioidosis in tropic environments.
Benzer Tezler
- Üç avcı tek av modelinin caputo kesirli türevi ve geri besleme kontrol değişkeni ile analizi
Analysis of three predator-one prey model with caputo fractional derivative and feedback control
SARE SAĞLAM
Yüksek Lisans
Türkçe
2024
MatematikSakarya ÜniversitesiMatematik Ana Bilim Dalı
PROF. DR. ÖMER FARUK GÖZÜKIZIL
- Sürekli ve ayrık popülasyon modellerinde Allee etkileri
Allee effects in continuous-time and discrete-time predator-prey system
PINAR BAYDEMİR DAŞTAN
Doktora
Türkçe
2024
MatematikTOBB Ekonomi ve Teknoloji ÜniversitesiMatematik Ana Bilim Dalı
PROF. DR. HÜSEYİN MERDAN
- Hopf bifurcation in a generalized Goodwin model with delay
Gecikmeli genelleştirilmiş Goodwin modelinde Hopf çatallanması
EYŞAN ŞANS
Yüksek Lisans
İngilizce
2024
Matematikİstanbul Teknik ÜniversitesiMatematik Mühendisliği Ana Bilim Dalı
DOÇ. DR. CİHANGİR ÖZEMİR
- Üstel olarak zayıflayan hafıza içeren bir av-iki avcı etkileşimlerinin bir matematiksel modellemesi
A mathematical modelling of one prey-two predator interactions involving exponentially weakening memory effect
ZEYNEP YILMAZ
- Salgın hastalıklarda aşı ve karantina etkisinin matematiksel modellemesi
Mathematical modeling of the effect of vaccination and quarantine in epidemic diseases
SEDA ÇELİK
Yüksek Lisans
Türkçe
2023
Matematikİstanbul Teknik ÜniversitesiMatematik Mühendisliği Ana Bilim Dalı
DOÇ. DR. SAADET SEHER ÖZER