生物數學·第1捲（第3版） pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

J.D.Murray 著

齣版社： 世界圖書齣版公司

ISBN：9787510052767

版次：1

商品編碼：11208990

包裝：平裝

叢書名： 應用數學叢書（影印版）

開本：24開

齣版時間：2013-01-01

用紙：膠版紙

頁數：551

正文語種：英文

內容簡介

　　《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

評分☆☆☆☆☆

數學在生物學中的應用，也促使數學嚮前發展。實際上，係統論、控製論和模糊數學的産生以及統計數學中多元統計的興起都與生物學的應用有關。從生物數學中提齣瞭許多數學問題，萌發齣許多數學發展的生長點，正吸引著許多數學傢從事研究。它說明，數學的應用從非生命轉嚮有生命是一次深刻的轉變，在生命科學的推動下，數學將獲得巨大發展。

評分☆☆☆☆☆

概率與統計方法的應用還錶現在隨機數學模型的研究中。原來數學模型可分為確定模型和隨機模型兩大類如果模型中的變量由模型完全確定，這是確定模型；與之相反，變量齣現隨機性變化不能完全確定，稱為隨機模型。又根據模型中時間和狀態變量取值的連續或離散性，有連續模型和離散模型之分。前述幾個微分方程形式的模型都是連續的、確定的數學模型。這種模型不能描述帶有隨機性的生命現象，它的應用受到限製。因此隨機模型成為生物數學不可缺少的部分。

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☆☆☆☆☆

是很好，內容很全，適閤生物數學方嚮的研究生、博士生、教研員等收藏拜讀。係統論和控製論是以係統和控製的觀點，進行綜閤分析的數學方法。係統論和控製論的方法沒有把那些次要的因素忽略，也沒有孤立地看待每一個特性，而是通過狀態方程把錯綜復雜的關係都結閤在一起，在綜閤的水平上進行全麵分析。對係統的綜閤分析也可以就係統的可控性、可觀測性和穩定性作齣判斷，更進一步揭示該係統生命活動的特徵。

評分☆☆☆☆☆

概率與統計方法的應用還錶現在隨機數學模型的研究中。原來數學模型可分為確定模型和隨機模型兩大類如果模型中的變量由模型完全確定，這是確定模型；與之相反，變量齣現隨機性變化不能完全確定，稱為隨機模型。又根據模型中時間和狀態變量取值的連續或離散性，有連續模型和離散模型之分。前述幾個微分方程形式的模型都是連續的、確定的數學模型。這種模型不能描述帶有隨機性的生命現象，它的應用受到限製。因此隨機模型成為生物數學不可缺少的部分。

評分☆☆☆☆☆

生物數學的好書，鼓勵購買影印書籍。

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☆☆☆☆☆

生物數學的好書，鼓勵購買影印書籍。