以隨機擾動項分別為Browan運動、分數Brown運動、Markovian過程和Poisson過程為主線，對種群模型進行數值計算理論的研究；主要針對年齡相關的種群模型、年齡相關擴散的種群模型和神經網路模型開展數值方法研究。採用Euler和半隱式Euler等數值方法，研究年齡相關隨機種群模型數值計算方法，給出數值解收斂和指數穩定的充分條件，並通過大量的數值算例驗證算法的有效性。為隨機種群發展系統求解構造出穩定的求解算法。主要包括四部分內容，一、預備知識；二、年齡相關隨機種群模型解的存在性和唯一性；三、年齡相關隨機種群模型的數值計算；四、隨機神經網路模型的數值計算。本書的內容全部是最新研究成果。
基本介紹
- 書名：隨機年齡結構種群系統
- 作者：張啟敏 李西寧
- 出版日期：2013年11月1日
- 語種：簡體中文, 英語
- 品牌：科學出版社
- 外文名：Stochastic Age-Structured Population Systems
- 出版社：科學出版社
- 頁數：229頁
- 開本：5
內容簡介,圖書目錄,
內容簡介
《隨機年齡結構種群系統(英文版)》以隨機擾動項分別為Browan運動、分數Brown運動、Markovian過程和Poisson過程為主線，對種群模型進行數值計算理論的研究；主要針對年齡相關的種群模型、年齡相關擴散的種群模型和神經網路模型開展數值方法研究。
圖書目錄
《生物數學叢書》序
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 formula
1.7 Moment inequalities
1.8 Gronwall—type inequalities
Chapter 2 Existence， 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—implicit Euler method for
stochastic age—dependent population equations with
Markovian 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 Poisson 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 Lemmas 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 Introduction
14.2 Preliminaries and approximation
14.3 Lemmas
14.4 Numerical simulation example
Bibliography
Index
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 formula
1.7 Moment inequalities
1.8 Gronwall—type inequalities
Chapter 2 Existence， 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—implicit Euler method for
stochastic age—dependent population equations with
Markovian 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 Poisson 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 Lemmas 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 Introduction
14.2 Preliminaries and approximation
14.3 Lemmas
14.4 Numerical simulation example
Bibliography
Index
