Evolution of Biological Systems in Random Media: Limit Theorems and Stability

2003. Auflage 2003
ISBN: 978-1-4020-1554-0
Verlag: Springer

Buch, Englisch, Band 18, 218 Seiten, Format (B × H): 165 mm x 248 mm, Gewicht: 1140 g

Reihe: Mathematical Modelling: Theory and Applications

The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)), xE X. Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R, respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y.

Zielgruppe

Research

Autoren/Hrsg.

Swishchuk, Anatoly

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Wirtschaftswissenschaften Volkswirtschaftslehre Wirtschaftspolitik, politische Ökonomie
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Vorklinische Medizin: Grundlagenfächer Humangenetik
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Demographie, Demoskopie
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Naturwissenschaften Biowissenschaften Molekularbiologie
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Arbeitsmarkt

Inhaltsverzeichnis

1 Random Media.- 2 Limit Theorems for Difference Equations in Random Media.- 3 Epidemic Models.- 4 Genetic Selection Models.- 5 Branching Models.- 6 Demographic Models.- 7 Logistic Growth Models.- 8 Predator-Prey Models.