陈兰荪主编的《随机年龄结构种群系统》 is intend to give an introduction to the theory of stochastic agestructured population dynamic system which has received strong attention in recent years because of its interesting structure and its usefulness in various applied fields.

《随机年龄结构种群系统》的主编是陈兰荪。

《随机年龄结构种群系统》mainly study the numerical method of the population with a variety of noise models. Including the author's research. The given numerical methods and the conclusions provide new ideas and theoretical basis for stochastic evolution-type partial differential equations numerical calculation, but also to the value of the stochastic population system provides a reliable method. Provide a strong basis to explore epidemics, ecological environment and the protection of the population.Since the dynamics method study of the life sciences was first proposed, and the logistic model, prey model and infectious diseases model was considered to be the most famous model. Subsequently, on the basis of the modeling, age structure,time-lag， migration, random interference of environment, intraspecific competition for resources， interspecific competition for resources have been considered. With the development of computer technology of the sixties and seventies years, the awareness of the seriousness of the ecological crisis to promote the further development of mathematical biology. To solve the five major worldwide problem: resources,energy, environment, population and food are also related on Ecology

Preface

Chapter 1 Introduction

1.1 Introduction

1.2 Basic notations of probability theory

1.3 Stochastic processes

1.4 Brownian motions

1.5 Stochastic integrals

1.6 Ito's formu]a

1.7 Moment inequalities

1.8 Gronwall-type inequalities

Chapter 2 Existences uniqueness and exponential stability for

       stochastic age-dependent population

2.1 Introduction

2.2 Assumptions and preliminaries

2.3 Existence and uniqueness of solutions

   2.3.1 Uniqueness of solutions

   2.3.2 Existence of strong solutions

2.4 Stability of strong solutions

Chapter 3 Existence and uniqueness for stochastic age-structured

       population system with diffusion

3.1 Introduction

3.2 Euler approximation and main result

3.3 Existence and uniqueness of solutions

   3.3.1 Uniqueness of solutions

   3.3.2 Existence of strong solutions

3.4 Numerical simulation example

Chapter 4 Existence and uniqueness for stochastic age-dependent

       population with fractional Brownian motion

4.1 Introduction

4.2 Preliminaries

4.3 Existence and uniqueness of solutions

Chapter 5 Convergence of the Euler scheme for stochastic functional

       partial differential equations

5.1 Introduction

5.2 Preliminaries and the Euler approximation

5.3 The main results

5.4 Numerical simulation example

Chapter 6 Numerical analysis for stochastic age-dependent

       population equations

6.1 Introduction

6.2 Preliminaries and the Euler approximation

6.3 The main results

Chapter 7 Convergence of numerical solutions to stochastic

       age-structured population system with diffusion

7.1 Introduction

7.2 Preliminaries and approximation

7.3 The main results

7.4 Numerical simulation example

Chapter 8 Exponential stability of numerical solutions to a stochas-

       tic age-structured population system with diffusion

8.1 Introduction

8.2 Preliminaries and Euler approximation

8.3 The main results

8.4 Numerical simulation example

Chapter 9 Numerical analysis for stochastic age-dependent popula-

       tion equations with fractional Brownian motion

9.1 Introduction

9.2 Preliminaries and the Euler approximation 

9.3 The main results 

9.4 Numerical simulation example 

Chapter 10 Convergence of the semi-lmplicit Euler method for

        stochastic age-dependent population equations with

        Markovlan switching 

10.1 Introduction 

10.2 Preliminaries and semi-implicit approximation 

10.3 Several lemmas 

10.4 Main results

Chapter 11 Convergence of numerical solutions to stochastic

        age-dependent population equations with Poisson jump

        and Markovian switching

11.1 Introduction

11.2 Preliminaries and semi-implicit approximation

11.3 Several lemmas

11.4 Main results

Chapter 12 Numerical analysis for stochastic delay neural networks

        with Poissou jump

12.1 Introduction

12.2 Preliminaries and the Euler approximation

12.3 The main results

12.4 Numerical simulation example

Chapter 13 Convergence of numerical solutions to stochastic delay

        neural networks with Poisson jump and Markov

        switching

13.1 Introduction

13.2 Preliminaries and the Euler approximation

13.3 Lennnas and corollaries ,

13.4 Convergence with the local Lipschitz condition :

Chapter 14 Exponential stability of numerical solutions to a

        stochastic delay neural networks 

14.1 Iutroduction 

14.2 Preliminaries and approximation 

14.3 Lemnlas 

14.4 Numerical simulation example 

Bibliography 

Index