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

Anatoly Swishchuk, Jianhong Wu (Autoren)

Buch | Softcover

218 Seiten

2010 | Softcover reprint of the original 1st ed. 2003
Springer (Verlag)
978-90-481-6398-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	7.12.2010
Reihe/Serie	Mathematical Modelling: Theory and Applications ; 18
Zusatzinfo	XX, 218 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Studium ► 2. Studienabschnitt (Klinik) ► Humangenetik
	Studium ► Querschnittsbereiche ► Epidemiologie / Med. Biometrie
	Naturwissenschaften ► Biologie
	Wirtschaft
ISBN-10	90-481-6398-6 / 9048163986
ISBN-13	978-90-481-6398-4 / 9789048163984
Zustand	Neuware