Evolution of Biological Systems in Random Media: Limit Theorems and Stability / Edition 1

Evolution of Biological Systems in Random Media: Limit Theorems and Stability / Edition 1

by Anatoly Swishchuk, Jianhong Wu
     
 

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

See more details below

Overview

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.

Product Details

ISBN-13:
9781402015540
Publisher:
Springer Netherlands
Publication date:
10/31/2003
Series:
Mathematical Modelling: Theory and Applications Series, #18
Edition description:
2003
Pages:
218
Product dimensions:
9.21(w) x 6.14(h) x 0.56(d)

Meet the Author

Table of Contents

Preface. List of Notations.
1: Random Media. 1.1. Markov Chains. 1.2. Ergodicity and Reducibility of Markov Chains. 1.3. Markov Renewal Processes. 1.4. Semi-Markov Processes. 1.5. Jump Markov Processes. 1.6. Wiener Processes and Diffusion Processes. 1.7. Martingales. 1.8. Semigroups of Operators and their Generators. 1.9. Martingale Characterization of Markov and Semi-Markov Processes. 1.10. General Representation and Measurability of Biological Systems in Random Media.
2: Limit Theorems for Difference Equations in Random Media. 2.1. Limit Theorems for Random Evolutions. 2.2. Averaging of Difference Equations in Random Media. 2.3. Diffusion Approximation of Difference Equations in Random Media. 2.4. Normal Deviations of Difference Equations in Random Media. 2.5. Merging of Difference Equations in Random Media. 2.6. Stability of Difference Equations in Random Media. 2.7. Limit Theorems for Vector Difference Equations in Random Media.
3: Epidemic Models. 3.1. Deterministic Epidemic Models. 3.2. Shastic Epidemic Model (Epidemic Model in Random Media). 3.3. Averaging of Epidemic Model in Random Media. 3.4. Merging of Epidemic Models in Random Media. 3.5. Diffusion Approximation of Epidemic Models in Random Media. 3.6. Normal Deviations of Epidemic Model in Random Media. 3.7. Shastic Stability of Epidemic Model.
4: Genetic Selection Models. 4.1. Deterministic Genetic Selection Models. 4.2. Shastic Genetic Selection Model (Genetic Selection Model in Random Media). 4.3.4.4. Merging of Slow Genetic Selection Model in Random Media. 4.5. Diffusion Approximation of Slow Genetic Selection Model in Random Media. 4.6. Normal Deviations of Slow Genetic Selection Model in Random Media. 4.7. Shastic Stability of Slow Genetic Selection Model.
5: Branching Models. 5.1. Branching Models with Deterministic Generating Function. 5.2. Branching Models in Random Media. 5.3. Averaging of Branching Models in Random Media. 5.4. Merging of Branching Model in Random Media. 5.5. Diffusion Approximation of Branching Process in Random Media. 5.6. Normal Deviations of Branching Process in Random Media. 5.7. Shastic Stability of Branching Model in Averaging and Diffusion Approximation Schemes.
6: Demographic Models. 6.1. Deterministic Demographic Model. 6.2. Shastic Demographic Models (Demographic Models in Random Media). 6.3. Averaging of Demographic Models in Random Media. 6.4. Merging of Demographic Model. 6.5. Diffusion Approximation of Demographic Model. 6.6. Normal Deviations of Demographic Models in Random Media. 6.7. Shastic Stability of Demographic Model in Averaging and Diffusion Approximation Schemes.
7: Logistic Growth Models. 7.1. Deterministic Logistic Growth Model. 7.2. Shastic Logistic Growth Model (Logistic Growth Model in Random Media). 7.3. Averaging of Logistic Growth Model in Random Media. 7.4. Merging of Logistic Growth Model in Random Media. 7.5. Diffusion Approximation of Logistic Growth Model in Random Media. 7.6. Normal Deviations of Logistic Growth Model in Random Media. 7.7. Shastic Stability of Logistic Growth Model in Averaging and Diffusion Approximation Schemes.
8: Predator-Prey Models. 8.1. Deterministic Predator-Prey Model. 8.2. Shastic Predator-Prey Model (Predator-Prey Model in Random Media). 8.3. Averaging of Predator-Prey Model in Random Media. 8.4. Merging of Predator-Prey Model. 8.5. Diffusion Approximation of Predator-Prey Model. 8.6. Normal Deviations of Predator-Prey Model in Random Media. 8.7. Shastic Stability of Predator-Prey Model in Averaging and Diffusion Approximation Schemes.
Bibliography. Index.

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >