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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Evolution of Biological Systems in Random Media: Limit Theorems and Stability

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

Swishchuk, Anatoly
Jianhong Wu

Hardcover

Series: Mathematical Modelling: Theory and Applications, Book 18

BiologyGeneral MathematicsProbability & Statistics

ISBN10: 1402015542
ISBN13: 9781402015540
Publisher: Springer Nature
Published: Oct 31 2003
Pages: 218
Weight: 1.11
Height: 0.74 Width: 6.48 Depth: 9.76
Language: English
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.

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