2003, ISBN: 9781402015540

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 m… More...

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. Buch (fremdspr.) Anatoly Swishchuk#Jianhong Wu gebundene Ausgabe, Springer Netherland, 31.10.2003, Springer Netherland, 2003<

ISBN: 9781402015540

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 m… More...

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. Books > Science & Nature > Math & Physics > Mathematics List_Books, [PU: Springer]<

ISBN: 9781402015540

This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results f… More...

This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This book contains: -New stochastic non-linear models of biological systems, such as biological systems in random media: epidemic, genetic selection, demography, branching, logistic growth and predator-prey models; -New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1); -New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability; -New approach to the study of stochastic biological systems in random media such as random evolution approach. Evolution of Biological Systems in Random Media: Limit Theorems and Stability Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer Netherlands<

ISBN: 9781402015540

Hardcover

Paperback / softback. New. We do try to convince the reader that there is a mathematical basis consisting of theories of bounds of linear functions and linear diophantine equations, that… More...

Paperback / softback. New. We do try to convince the reader that there is a mathematical basis consisting of theories of bounds of linear functions and linear diophantine equations, that levels and direction vectors are concepts that arise rather natu rally, that different dependence tests are really special cases of some general tests, and so on., 6, Hardback. New. This concise, fast-paced text introduces the concepts and applications behind plane networks. It presents fundamental material from linear algebra and differential equations, and offers several different applications of the continuous theory. Practical problems, supported by MATLAB files, underscore the theory, 6, Hardback. New. Containing stochastic non-linear models of biological systems, this book in biomathematics presents results for scalar and vector difference equations in random media with applications to the stochastic biological systems. It also offers an approach to the study of stochastic biological systems in random media such as random evolution approach., 6<