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　　《生物数学·第1卷（第3版）》是近代生物数学方面的名著。这是第一卷，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。

目录

contents, volume i
preface to the third edition
preface to the first edition
1. continuous population models for single species
1.1 continuous growth models
1.2 insect outbreak model： spruce budworm
1.3 delay models
1.4 linear analysis of delay population models： periodic solutions
1.5 delay models in physiology： periodic dynamic diseases
1.6 harvesting a single natural population
1.7 population model with age distribution
exercises

2. discrete population models for a single species
2.1 introduction： simple models
2.2 cobwebbing： a graphical procedure of solution
2.3 discrete logistic-type model： chaos
2.4 stability, periodic solutions and bifurcations
2.5 discrete delay models
2.6 fishery management model
.2.7 ecological implications and caveats
2.8 tumour cell growth
exercises

3. models for interacting populations
3.1 predator-prey models： lotka-volterra systems
3.2 complexity and stability
3.3 realistic predator-prey models
3.4 analysis of a predator-prey model with limit cycle periodic behaviour： parameter domains of stability
3.5 competition models： competitive exclusion principle
3.6 mutualism or symbiosis
3.7 general models and cautionary remarks
3.8 threshold phenomena
3.9 discrete growth models for interacting populations
3.10 predator-prey models： detailed analysis
exercises

4. temperature-dependent sex determination （tsd）
4.1 biological introduction and historical asides on the crocodilia.
4.2 nesting assumptions and simple population model
4.3 age-structured population model for crocodilia
4.4 density-dependent age-structured model equations
4.5 stability of the female population in wet marsh region l
4.6 sex ratio and survivorship
4.7 temperature-dependent sex determination （tsd） versus genetic sex determination （gsd）
4.8 related aspects on sex determination
exercise

5. modelling the dynamics of marital interaction： divorce prediction and marriage repair
5.1 psychological background and data： gottman and levenson methodology
5.2 marital typology and modelling motivation
5.3 modelling strategy and the model equations
5.4 steady states and stability
5.5 practical results from the model
5.6 benefits, implications and marriage repair scenarios
6. reaction kinetics
6.1 enzyme kinetics： basic enzyme reaction
6.2 transient time estimates and nondimensionalisation
6.3 michaelis-menten quasi-steady state analysis
6.4 suicide substrate kinetics
6.5 cooperative phenomena
6.6 autocatalysis, activation and inhibition
6.7 multiple steady states, mushrooms and isolas
exercises

7. biological oscillators and switches
7.1 motivation, brief history and background
7.2 feedback control mechanisms
7.3 oscillators and switches with two or more species： general qualitative results
7.4 simple two-species oscillators： parameter domain determination for oscillations
7.5 hodgkin-huxley theory of nerve membranes：fitzhugh-nagumo model
7.6 modelling the control of testosterone secretion and chemical castration
exercises

8. bz oscillating reactions
8.1 belousov reaction and the field-koros-noyes （fkn） model
8.2 linear stability analysis of the fkn model and existence of limit cycle solutions
8.3 nonlocal stability of the fkn model
8.4 relaxation oscillators： approximation for the belousov-zhabotinskii reaction
8.5 analysis of a relaxation model for limit cycle oscillations in the belousov-zhabotinskii reaction
exercises

9. perturbed and coupled oscillators and black holes
9.1 phase resetting in oscillators
9.2 phase resetting curves
9.3 black holes
9.4 black holes in real biological oscillators
9.5 coupled oscillators： motivation and model system
9.6 phase locking of oscillations： synchronisation in fireflies
9.7 singular perturbation analysis： preliminary transformation
9.8 singular perturbation analysis： transformed system
9.9 singular perturbation analysis： two-time expansion
9.10 analysis of the phase shift equation and application to coupled belousov-zhabotinskii reactions
exercises

10. dynamics of infectious diseases
10.1 historical aside on epidemics
10.2 simple epidemic models and practical applications
10.3 modelling venereal diseases
10.4 multi-group model for gonorrhea and its control
10.5 aids： modelling the transmission dynamics of the human immunodeficiency virus （hiv）
10.6 hiv： modelling combination drug therapy
10.7 delay model for hiv infection with drug therapy
10.8 modelling the population dynamics of acquired immunity to parasite infection
10.9 age-dependent epidemic model and threshold criterion
10.10 simple drug use epidemic model and threshold analysis
10.11 bovine tuberculosis infection in badgers and caule
10.12 modelling control strategies for bovine tuberculosis in badgers and cattle
exercises

11. reaction diffusion, chemotaxis, and noniocal mechanisms
11.1 simple random walk and derivation of the diffusion equation
11.2 reaction diffusion equations
11.3 models for animal dispersal
11.4 chemotaxis
11.5 nonlocal effects and long range diffusion
11.6 cell potential and energy approach to diffusion and long range effects
exercises

12. oscillator-generated wave phenomena
12. i belousov-zhabotinskii reaction kinematic waves
12.2 central pattern generator： experimental facts in the swimming of fish
12.3 mathematical model for the central pattern generator
12.4 analysis of the phase coupled model system
exercises

13. biological waves： single-species models
13. l background and the travelling waveform
13.2 fisher-kolmogoroff equation and propagating wave solutions
13.3 asymptotic solution and stability of wavefront solutions of the fisher-kolmogoroff equation
13.4 density-dependent diffusion-reaction diffusion models and some exact solutions
13.5 waves in models with multi-steady state kinetics： spread and control of an insect population
13.6 calcium waves on amphibian eggs： activation waves on medaka eggs
13.7 invasion wavespeeds with dispersive variability
13.8 species invasion and range expansion
exercises

14. use and abuse of fractals
14.1 fractals： basic concepts and biological relevance
14.2 examples of fractals and their generation
14.3 fractal dimension： concepts and methods of calculation
14.4 fractals or space-filling?
appendices
a. phase plane analysis
b. routh-hurwitz conditions, jury conditions, descartes'
rule of signs, and exact solutions of a cubic
b.1 polynomials and conditions
b.2 descartes' rule of signs
b.3 roots of a general cubic polynomial
bibliography
index
contents, volume ii
j.d. murray： mathematical biology, ii： spatial models and biomedical applications
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 x-co reaction diffusion systems

2. spatial pattern formation with reaction diffusion systems
2.1 role of pattern in biology
2.2 reaction diffusion （turing） 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, turing 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

3. animal coat patterns and other practical applications of reactiondiffusion mechanisms
3.1 mammalian coat patterns--'how the leopard got its spots'
3.2 teratologies： examples of animal coat pa 生物数学·第1卷（第3版） 电子书 下载 mobi epub pdf txt

评分☆☆☆☆☆

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。618活动时候买的，价格实惠，感谢京东，以后买书就上这了。

评分☆☆☆☆☆

很有意思的

评分☆☆☆☆☆

上述各种生物数学方法的应用，对生物学产生重大影响。20世纪50年代以来，生物学突飞猛进地发展，多种学科向生物学渗透，从不同角度展现生命物质运动的矛盾，数学以定量的形式把这些矛盾的实质体现出来。从而能够使用数学工具进行分析；能够输入电脑进行精确的运算；还能把来自名方面的因素联系在一起，通过综合分析阐明生命活动的机制。

评分☆☆☆☆☆

继托姆之后，跃变论不断地发展。例如塞曼又提出初级波和二级波的新理论。

评分☆☆☆☆☆

概率与统计方法的应用还表现在随机数学模型的研究中。原来数学模型可分为确定模型和随机模型两大类如果模型中的变量由模型完全确定，这是确定模型；与之相反，变量出现随机性变化不能完全确定，称为随机模型。又根据模型中时间和状态变量取值的连续或离散性，有连续模型和离散模型之分。前述几个微分方程形式的模型都是连续的、确定的数学模型。这种模型不能描述带有随机性的生命现象，它的应用受到限制。因此随机模型成为生物数学不可缺少的部分。

评分☆☆☆☆☆

60年代末，法国数学家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，他的理论称为突变理论。

评分☆☆☆☆☆

数学在生物学中的应用，也促使数学向前发展。实际上，系统论、控制论和模糊数学的产生以及统计数学中多元统计的兴起都与生物学的应用有关。从生物数学中提出了许多数学问题，萌发出许多数学发展的生长点，正吸引着许多数学家从事研究。它说明，数学的应用从非生命转向有生命是一次深刻的转变，在生命科学的推动下，数学将获得巨大发展。

评分☆☆☆☆☆

很有意思的

评分☆☆☆☆☆

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。618活动时候买的，价格实惠，感谢京东，以后买书就上这了。

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