生物数学

出版时间：2013-1  出版社：世界图书出版公司  
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作者简介

作者：（美国）莫里（Murray J.D.）

书籍目录

contents, volume ipreface to the third editionpreface to the first edition1. continuous population models for single species1.1 continuous growth models1.2 insect outbreak model： spruce budworm1.3 delay models1.4 linear analysis of delay population models： periodic solutions1.5 delay models in physiology： periodic dynamic diseases1.6 harvesting a single natural population1.7 population model with age distributionexercises2. discrete population models for a single species2.1 introduction： simple models2.2 cobwebbing： a graphical procedure of solution2.3 discrete logistic-type model： chaos2.4 stability, periodic solutions and bifurcations2.5 discrete delay models2.6 fishery management model.2.7 ecological implications and caveats2.8 tumour cell growthexercises3. models for interacting populations3.1 predator-prey models： lotka-volterra systems3.2 complexity and stability3.3 realistic predator-prey models3.4 analysis of a predator-prey model with limit cycle periodic behaviour： parameter domains of stability3.5 competition models： competitive exclusion principle3.6 mutualism or symbiosis3.7 general models and cautionary remarks3.8 threshold phenomena3.9 discrete growth models for interacting populations3.10 predator-prey models： detailed analysisexercises4. temperature-dependent sex determination （tsd）4.1 biological introduction and historical asides on the crocodilia.4.2 nesting assumptions and simple population model4.3 age-structured population model for crocodilia4.4 density-dependent age-structured model equations4.5 stability of the female population in wet marsh region l4.6 sex ratio and survivorship4.7 temperature-dependent sex determination （tsd） versus genetic sex determination （gsd）4.8 related aspects on sex determinationexercise5. modelling the dynamics of marital interaction： divorce prediction and marriage repair5.1 psychological background and data： gottman and levenson methodology5.2 marital typology and modelling motivation5.3 modelling strategy and the model equations5.4 steady states and stability5.5 practical results from the model5.6 benefits, implications and marriage repair scenarios6. reaction kinetics6.1 enzyme kinetics： basic enzyme reaction6.2 transient time estimates and nondimensionalisation6.3 michaelis-menten quasi-steady state analysis6.4 suicide substrate kinetics6.5 cooperative phenomena6.6 autocatalysis, activation and inhibition6.7 multiple steady states, mushrooms and isolasexercises7. biological oscillators and switches7.1 motivation, brief history and background7.2 feedback control mechanisms7.3 oscillators and switches with two or more species： general qualitative results7.4 simple two-species oscillators： parameter domain determination for oscillations7.5 hodgkin-huxley theory of nerve membranes：fitzhugh-nagumo model7.6 modelling the control of testosterone secretion and chemical castrationexercises8. bz oscillating reactions8.1 belousov reaction and the field-koros-noyes （fkn） model8.2 linear stability analysis of the fkn model and existence of limit cycle solutions8.3 nonlocal stability of the fkn model8.4 relaxation oscillators： approximation for the belousov-zhabotinskii reaction8.5 analysis of a relaxation model for limit cycle oscillations in the belousov-zhabotinskii reactionexercises9. perturbed and coupled oscillators and black holes9.1 phase resetting in oscillators9.2 phase resetting curves9.3 black holes9.4 black holes in real biological oscillators9.5 coupled oscillators： motivation and model system9.6 phase locking of oscillations： synchronisation in fireflies9.7 singular perturbation analysis： preliminary transformation9.8 singular perturbation analysis： transformed system9.9 singular perturbation analysis： two-time expansion9.10 analysis of the phase shift equation and application to coupled belousov-zhabotinskii reactionsexercises10. dynamics of infectious diseases10.1 historical aside on epidemics10.2 simple epidemic models and practical applications10.3 modelling venereal diseases10.4 multi-group model for gonorrhea and its control10.5 aids： modelling the transmission dynamics of the human immunodeficiency virus （hiv）10.6 hiv： modelling combination drug therapy10.7 delay model for hiv infection with drug therapy10.8 modelling the population dynamics of acquired immunity to parasite infection10.9 age-dependent epidemic model and threshold criterion10.10 simple drug use epidemic model and threshold analysis10.11 bovine tuberculosis infection in badgers and caule10.12 modelling control strategies for bovine tuberculosis in badgers and cattleexercises11. reaction diffusion, chemotaxis, and noniocal mechanisms11.1 simple random walk and derivation of the diffusion equation11.2 reaction diffusion equations11.3 models for animal dispersal11.4 chemotaxis11.5 nonlocal effects and long range diffusion11.6 cell potential and energy approach to diffusion and long range effectsexercises12. oscillator-generated wave phenomena12. i belousov-zhabotinskii reaction kinematic waves12.2 central pattern generator： experimental facts in the swimming of fish12.3 mathematical model for the central pattern generator12.4 analysis of the phase coupled model systemexercises13. biological waves： single-species models13. l background and the travelling waveform13.2 fisher-kolmogoroff equation and propagating wave solutions13.3 asymptotic solution and stability of wavefront solutions of the fisher-kolmogoroff equation13.4 density-dependent diffusion-reaction diffusion models and some exact solutions13.5 waves in models with multi-steady state kinetics： spread and control of an insect population13.6 calcium waves on amphibian eggs： activation waves on medaka eggs13.7 invasion wavespeeds with dispersive variability13.8 species invasion and range expansionexercises14. use and abuse of fractals14.1 fractals： basic concepts and biological relevance14.2 examples of fractals and their generation14.3 fractal dimension： concepts and methods of calculation14.4 fractals or space-filling?appendicesa. phase plane analysisb. routh-hurwitz conditions, jury conditions, descartes'rule of signs, and exact solutions of a cubicb.1 polynomials and conditionsb.2 descartes' rule of signsb.3 roots of a general cubic polynomialbibliographyindexcontents, volume iij.d. murray： mathematical biology, ii： spatial models and biomedical applicationspreface to the third editionpreface to the first edition1. multi-species waves and practical applications1.1 intuitive expectations1.2 waves of pursuit and evasion in predator-prey systems1.3 competition model for the spatial spread of the grey squirrel in britain1.4 spread of genetically engineered organisms1.5 travelling fronts in the belousov-zhabotinskii reaction1.6 waves in excitable media1.7 travelling wave trains in reaction diffusion systems with oscillatory kinetics1.8 spiral waves1.9 spiral wave solutions of x-co reaction diffusion systems2. spatial pattern formation with reaction diffusion systems2.1 role of pattern in biology2.2 reaction diffusion （turing） mechanisms2.3 general conditions for diffusion-driven instability：linear stability analysis and evolution of spatial pattern2.4 detailed analysis of pattern initiation in a reaction diffusion mechanism2.5 dispersion relation, turing space, scale and geometry effects in pattern formation models2.6 mode selection and the dispersion relation2.7 pattern generation with single-species models： spatial heterogeneity with the spruce budworm model2.8 spatial patterns in scalar population interaction diffusion equations with convection： ecological control strategies2.9 nonexistence of spatial patterns in reaction diffusion systems： general and particular results3. animal coat patterns and other practical applications of reactiondiffusion mechanisms3.1 mammalian coat patterns--'how the leopard got its spots'3.2 teratologies： examples of animal coat pattern abnormalities3.3 a pattern formation mechanism for butterfly wing patterns3.4 modelling hair patterns in a whorl in acetabularia4. pattern formation on growing domains： alligators and snakes4. i stripe pattern formation in the alligator： experiments4.2 modelling concepts： determining the time of stripe formation4.3 stripes and shadow stripes on the alligator4.4 spatial patterning of teeth primordia in the alligator：background and relevance4.5 biology of tooth initiation4.6 modelling tooth primordium initiation： background4.7 model mechanism for alligator teeth patterning4.8 results and comparison with experimental data4.9 prediction experiments4.10 concluding remarks on alligator tooth spatial patterning4.11 pigmentation pattern formation on snakes4.12 cell-chemotaxis model mechanism4.13 simple and complex snake pattern elements4.14 propagating pattern generation with the celi-chemotaxis system5. bacterial patterns and chemotaxis5.1 background and experimental results5.2 model mechanism for e. coli in the semi-solid experiments5.3 liquid phase model： intuitive analysis of pattern formation5.4 interpretation of the analytical results and numerical solutions5.5 semi-solid phase model mechanism for s. typhimurium5.6 linear analysis of the basic semi-solid model5.7 brief outline and results of the nonlinear analysis5.8 simulation results, parameter spaces, basic patterns5.9 numerical results with initial conditions from the experiments5.10 swarm ring patterns with the semi-solid phase model mechanism5.11 branching patterns in bacillus subtilis6. mechanical theory for generating pattern and form in development6.1 introduction, motivation and background biology6.2 mechanical model for mesenchymal morphogenesis6.3 linear analysis, dispersion relation and pattern formation potential6.4 simple mechanical models which generate spatial patterns with complex dispersion relations6.5 periodic patterns of feather germs6.6 cartilage condensation in limb morphogenesis and morphogenetic rules6.7 embryonic fingerprint formation6.8 mechanochemical model for the epidermis6.9 formation of microvilli6.10 complex pattern formation and tissue interaction models7. evolution, morphogenetic laws, developmental constraints and teratologies7.1 evolution and morphogenesis7.2 evolution and morphogenetic rules in cartilage formation in the vertebrate limb7.3 teratologies （monsters）7.4 developmental constraints, morphogenetic rules and the consequences for evolution8.a mechanical theory of vascular network formation8.1 biological background and motivation8.2 cell-extracellular matrix interactions for vasculogenesis8.3 parameter values8.4 analysis of the model equations8.5 network patterns： numerical simulations and conclusions9. epidermal wound healing9.1 brief history of wound healing9.2 biological background： epidermal wounds9.3 model for epidermal wound healing9.4 nondimensional form, linear stability and parameter values9.5 numerical solution for the epidermal wound repair model9.6 travelling wave solutions for the epidermal model9.7 clinical implications of the epidermal wound model9.8 mechanisms of epidermal repair in embryos9.9 actin alignment in embryonic wounds： a mechanical model9.10 mechanical model with stress alignment of the actin filaments in two dimensions10. dermal wound healing10.1 background and motivation---general and biological10.2 logic of wound healing and initial models10.3 brief review of subsequent developments10.4 model for fibroblast-driven wound healing： residual strain and tissue remodelling10.5 solutions of the model equation solutions and comparison with experiment10.6 wound healing model of cook （1995）10.7 matrix secretion and degradation10.8 cell movement in an oriented environment10.9 model system for dermal wound healing with tissue structure10.10 one-dimensional model for the structure of pathological scars10.11 open problems in wound healing10.12 concluding remarks on wound healing11. growth and control of brain tumours11.1 medical background11.2 basic mathematical model of glioma growth and invasion11.3 tumour spread in vitro： parameter estimation11.4 tumour invasion in the rat brain11.5 tumour invasion in the human brain11.6 modelling treatment scenarios： general comments11.7 modelling tumour resection （removal） in homogeneous tissue11.8 analytical solution for tumour recurrence after resection11.9 modelling surgical resection with brain tissue heterogeneity11.10 modelling the effect of chemotherapy on tumour growth11.11 modeling tumour polyclonality and cell mutation12. neural models of pattern formation12.1 spatial patterning in neural firing with a simple activation-inhibition model12.2 a mcchanism for stripe formation in the visual cortex12.3 a model for the brain mechanism underlying visual hallucination patterns12.4 neural activity model for shell patterns12.5 shamanism and rock art13. geographic spread and control of epidemics13.1 simple model for the spatial spread of an epidemic13.2 spread of the black death in europe 1347-135013.3 brief history of rabies： facts and myths13.4 the spatial spread of rabies among foxes i： background and simple model13.5 spatial spread of rabies among foxes ii：three-species （sir） model13.6 control strategy based on wave propagation into a non-epidemic region： estimate of width of a rabies barrier13.7 analytic approximation for the width of the rabies control break13.8 two-dimensional epizootic fronts and effects ot variable fox densitics： quantitative predictions for a rabies outbreak in england13.9 effect of fox immunity on spatial spread of rabies14. wolf territoriality, wolf-deer interaction and survival14.1 introduction and wolf ecology14.2 models for wolf pack territory formation： single pack--home range model14.3 multi-wolf pack territorial model14.4 wolf-deer predator-prey model14.5 concluding remarks on-wolf territoriality and deer survival14.6 coyote home range patterns14.7 chippewa and sioux intertribal conflict c1750-1850appendixa. general results for the laplacian operator in bounded domainsbibliographyindex

章节摘录

版权页：   插图：   (Volatile, Validating and Avoiding), and for the two unstable marriages (Hostile a Hostile-Detached). For heuristic purposes we used the two-slope model of the influen function. We now discuss this figure. The top three graphs represent the influence fu tions for the three regulated marriages. The Validators have an influence function creates an influence toward negativity in a spouse if the partner's behaviour is negat and an influence toward positivity if the partner's behaviour is positive. Volatile a Conflict-Avoider influence functions appear to be, respectively, one half of the valid tors, with volatiles having the right half of the curve with a slope close to zero, and Conflict-Avoiders having the left half with a slope near zero. This observation of ing functions is summarised in the third column, labelled theoretical influence function Now examine the influence functions for the Hostile and the Hostile-Detached couple It looks as if these data would support a mismatch hypothesis. Hostile couples appear have mixed a Validator husband influence function with a Conflict-Avoider wife ence function, and Hostile-Detached couples appear to have mixed a Validator influence function with a Volatile wife influence function. From examining the data, we can propose that validating couples were able to fluence their spouses with both positive or negative behaviour; positive behaviour a positive sloping influence while negative behaviour also had a positive sloping ence. This means that the negative horizontal axis values had a negative influence -the-positive-horizontal axis values had a positive influence. For validators, across ttwhole range of RCISS point values, the slope of the influence function was a constsupwardly sloping straight line. The data might have been generated by the process in validating low risk marriages there is_a uniform slope of the influence function both positive and negative values: Overall negative behaviour has a negative influenewhile positive behaviour has a positive influence in low risk marriages. Here we see a full range of emotional balance is possible in the interaction.However, avoiders at volatile couples were nearly opposite in the shape of their influence functions. Avoide influenced one another only with positivity (the slope was flat in the negative RCIS point ranges), while volatile couples influenced one another primarily with negativi (the slope was flat in the positive RCISS point ranges). The influence function of avoiding couple is nearly the reverse of that of the volatile couple. Mismatch Theory: The Possibility that Unstable Marriages Are the Results of Failed Attempts at Creating a Pure Type The shape of the influence curves leads us to propose that the data on marital stabi ity and instability can be organized by the rather simple hypothesis that Hostile ar Hostile-detached couples are simply failures tO create a stable adaptation to that is either Volatile, Validating, or Avoiding. In other words, the hypothesis is that longitudinal marital stability results are an artifact of the prior inability of the couple accommodate to. one another and have one of the three types of marriage. For exampl in the unstable marriage, a person who is more suited to a Volatile or a Conflict-Avoidir marriage may have married one who wishes a validating marriage. Their influence fun tions are simply mismatched.

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《生物数学(第1卷)(第3版)(英文版)》由世界图书出版公司北京公司出版。