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内容简介

　　《生物数学（第2卷·第3版）》近代生物数学方面的名著。第三版，在原来版本的基础上做了全面修订。近年来这个科目的茁壮成长和新知识点的不断涌现，新的版本将原来的一卷集分成上下两卷，扩大了知识容量，第二卷绝大多数是新增知识点。书中对生物学中的反应扩散方程和形态发生学的数学理论及最新研究成果作了全面介绍，是学习与研究生物数学的一部不可多得的参考书。

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目录

CONTENTS,VOLUME Ⅱ
Preface to the Third Edition
Preface to the First Edition

1.Multi-Species Waves and Practical Applications
1.1 Intuitive Expectations
1.2 Waves of Pursuit and Evasion in Predator-Prey Systems
1.3 Competition Model for the Spatial Spread of the Grey Squirrel in Britain
1.4 Spread of Genetically Engineered Organisms
1.5 Travelling Fronts in the Belousov-Zhabotinskii Reaction
1.6 Waves in Excitable Media
1.7 Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics
1.8 Spiral Waves
1.9 Spiral Wave Solutions of Reaction Diffusion Systems
Exercises

2.Spatial Pattern Formation with Reaction Diffusion Systems
2.1 Role of Pattern in Biology
2.2 Reaction Diffusion （Taring） Mechanisms
2.3 General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern
2.4 Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism
2.5 Dispersion Relation luring Space,Scale and Geometry Effects in Pattern Formation Models
2.6 Mode Selection and the Dispersion Relation
2.7 Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model
2.8 Spatial Patterns in Scalar Population Interaction Diffusion
Equations with Convection: Ecological Control Strategies
2.9 Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results
Exercises

3.Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms
3.1 Mammalian Coat Patterns——How the Leopard Got Its Spots
3.2 Teratologies: Examples of Animal Coat Pattern Abnormalities
3.3 A Pattern Formation Mechanism for Butterfly Wing Patterns
3.4 Modelling Hair Patterns in a Whorl in Acetabularia

4.Pattern Formation on Growing Domains: Alligators and Snakes
4.1 Stripe Pattern Formation in the Alligator: Experiments
4.2 Modelling Concepts: Determining the Time of Stripe Formation
4.3 Stripes and Shadow Stripes on the Alligator
4.4 Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance
4.5 Biology of Tooth Initiation
4.6 Modelling Tooth Primordium Initiation: Background
4.7 Model Mechanism for Alligator Teeth Patterning
4.8 Results and Comparison with Experimental Data
4.9 Prediction Experiments
4.10 Concluding Remarks on Alligator Tooth Spatial Patterning
4.11 Pigmentation Pattern Formation on Snakes
4.12 Cell-Chemotaxis Model Mechanism
4.13 Simple and Complex Snake Pattern Elements
4.14 Propagating Pattern Generation with the Cell-Chemotaxis System

5.Bacterial Patterns and Chemotaxis
5.1 Background and Experimental Results
5.2 Model Mechanism for E coil in the Semi-Solid Experiments
5.3 Liquid Phase Model: Intuitive Analysis of Pattern Formation
5.4 Interpretation of the Analytical Results and Numerical Solutions
5.5 Semi-Solid Phase Model Mechanism for S typhimurium
5.6 Linear Analysis of the Basic Semi-Solid Model
5.7 Brief Outline and Results of the Nonlinear Analysis
5.8 Simulation Results,Parameter Spaces and Basic Patterns
5.9 Numerical Results with Initial Conditions from the~Experiments
5.10 Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism
5.11 Branching Patterns in Bacillus subtilis

6.Mechanical Theory for Generating Pattern and Form in Development
6.1 Introduction,Motivation and Background Biology
6.2 Mechanical Model for Mesenchymal Morphogenesis
6.3 Linear Analysis,Dispersion Relation and Pattern Formation Potential
6.4 Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations
6.5 Periodic Patterns of Feather Germs
6.6 Cartilage Condensations in Limb Morphogenesis and Morphogenetic Rules
6.7 Embryonic Fingerprint Formation
6.8 Mechanochemical Model for the Epidermis
6.9 Formation of Microvilli
6.10 Complex Pattern Formation and Tissue Interaction Models
Exercises

7.Evolution,Morphogenetic Laws,Developmental Constraints and Teratologies
8.A Mechanical Theory of Vascular Network Formation
9.Epidermal Wound Healing
10.Dermal Wound Healing
11.Growth and Control of Brain Tumours
12.Neural Models of Pattern Formation
13.Geographic Spread and Control of Epidemics
14.Wolf Territoriality,Wolf-Deer Interaction and Survival
Appendix
A General Results for the Laplacian Operator in Bounded Domains
Bibliography
Index

前言/序言

生物数学（第2卷·第3版） [Mathematical Biology] 电子书 下载 mobi epub pdf txt

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很好的经典书，本册主要是研究的PDE模型的。印刷质量也还不错。

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学习学习

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比如描述生物种群增长的费尔许尔斯特-珀尔方程，就能够比较正确的表示种群增长的规律；通过描述捕食与被捕食两个种群相克关系的洛特卡-沃尔泰拉方程，从理论上说明：农药的滥用，在毒杀害虫的同时也杀死了害虫的天敌，从而常常导致害虫更猖獗地发生等。618活动时购入，核算下来差不多4折，很实惠，感谢京东，以后买书就上京东了。

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继R.托姆之后，跃变论不断地发展。例如E.C.塞曼又提出初级波和二级波的新理论。

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60年代末，法国数学家R.托姆从拓扑学提出一种几何模型，能够描绘多维不连续现象，他的理论称为突变论。

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学习学习

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知识是人类在实践中认识客观世界的成果。它可能包括事实，信息，描述或在教育和实践中获得的技能。它可能是关于理论的，也可能是关于实践的。在哲学中，关于知识的研究叫做认识论。知识的获取涉及到许多复杂的过程：感觉，交流，推理。知识也可以看成构成人类智慧的最根本的因素。

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当今的生物数学仍处于探索和发展阶段。生物数学的许多方法和理论还很不完善，它的应用虽然取得某些成功，但仍是低水平的、粗略的、甚至是勉强的。许多更复杂的生物学问题至今未能找到相应的数学方法进行研究。因此，生物数学还要从生物学的需要和特点，探求新方法、新手段和新的理论体系，还有待发展和完善。数学模型是能够表现和描述真实世界某些现象、特征和状况的数学系统。数学模型能定量地描述生命物质运动的过程，一个复杂的生物学问题借助数学模型能转变成一个数学问题，通过对数学模型的逻辑推理、求解和运算，就能够获得客观事物的有关结论，达到对生命现象进行研究的目的。

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书很好，印刷清晰，适合做生物数学的研究生，博士生，教研员等收藏拜读。描述生命现象的离散模型有两态和多态之分。马尔科夫链和莱斯利模型都属于多态；两态的模型应生物学的二元表现状态而产生。如神经兴奋沿着神经细胞的轴突，经过突触在阀的控制下传给另一个神经细胞，兴奋波的通过与否就是一个二元表现状态。1943年W.S.麦卡洛克和W.皮茨在布尔代数的基础上，首次给出描述神经传递现象的离散模型。此模型不断改进，并借助电脑加以实现，已做到模拟许多较复杂的神经功能，成为探索人类大脑思维奥秘的一个重要手段（见人工智能）。

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