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　　《生物數學·第1捲（第3版）》是近代生物數學方麵的名著。這是第一捲，第三版，在原來版本的基礎上做瞭全麵修訂。近年來這個科目的茁壯成長和新知識點的不斷湧現，新的版本將原來的一捲集分成上下兩捲，擴大瞭知識容量，第二捲絕大多數是新增知識點。書中對生物學中的反應擴散方程和形態發生學的數學理論及研究成果作瞭全麵介紹，是學習與研究生物數學的一部不可多得的參考書。

目錄

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 生物數學·第1捲（第3版） 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

生物數學的好書，鼓勵購買影印書籍。

評分☆☆☆☆☆

60年代末，法國數學傢托姆從拓撲學提齣一種幾何模型，能夠描繪多維不連續現象，他的理論稱為突變理論。

評分☆☆☆☆☆

好

評分☆☆☆☆☆

繼托姆之後，躍變論不斷地發展。例如塞曼又提齣初級波和二級波的新理論。

評分☆☆☆☆☆

書很厚，還沒仔細看看，嗬

評分☆☆☆☆☆

繼托姆之後，躍變論不斷地發展。例如塞曼又提齣初級波和二級波的新理論。

評分☆☆☆☆☆

上述各種生物數學方法的應用，對生物學産生重大影響。20世紀50年代以來，生物學突飛猛進地發展，多種學科嚮生物學滲透，從不同角度展現生命物質運動的矛盾，數學以定量的形式把這些矛盾的實質體現齣來。從而能夠使用數學工具進行分析；能夠輸入電腦進行精確的運算；還能把來自名方麵的因素聯係在一起，通過綜閤分析闡明生命活動的機製。

評分☆☆☆☆☆

繼托姆之後，躍變論不斷地發展。例如塞曼又提齣初級波和二級波的新理論。

評分☆☆☆☆☆

60年代末，法國數學傢托姆從拓撲學提齣一種幾何模型，能夠描繪多維不連續現象，他的理論稱為突變理論。

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