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�� periodicsolutions
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 periodicbehaviour�� 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 thecrocodilia.
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 geneticsex determination ��gsd��
4.8 related aspects on sex determination
exercise

5. modelling the dynamics of marital interaction�� divorceprediction and marriage repair
5.1 psychological background and data�� gottman and levensonmethodology
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�� generalqualitative results
7.4 simple two-species oscillators�� parameter domain determinationfor oscillations
7.5 hodgkin-huxley theory of nerve membranes��fitzhugh-nagumomodel
7.6 modelling the control of testosterone secretion and chemicalcastration
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 oflimit cycle solutions
8.3 nonlocal stability of the fkn model
8.4 relaxation oscillators�� approximation for thebelousov-zhabotinskii reaction
8.5 analysis of a relaxation model for limit cycle oscillations inthe 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 infireflies
9.7 singular perturbation analysis�� preliminarytransformation
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 tocoupled 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 humanimmunodeficiency 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 toparasite 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 inbadgers and cattle
exercises

11. reaction diffusion, chemotaxis, and noniocal mechanisms
11.1 simple random walk and derivation of the diffusionequation
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 rangeeffects
exercises

12. oscillator-generated wave phenomena
12. i belousov-zhabotinskii reaction kinematic waves
12.2 central pattern generator�� experimental facts in the swimmingof 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 wavesolutions
13.3 asymptotic solution and stability of wavefront solutions ofthe fisher-kolmogoroff equation
13.4 density-dependent diffusion-reaction diffusion models and someexact solutions
13.5 waves in models with multi-steady state kinetics�� spread andcontrol of an insect population
13.6 calcium waves on amphibian eggs�� activation waves on medakaeggs
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 andbiomedical 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 squirrelin 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 withoscillatory 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��linearstability analysis and evolution of spatial pattern
2.4 detailed analysis of pattern initiation in a reaction diffusionmechanism
2.5 dispersion relation, turing space, scale and geometry effectsin pattern formation models
2.6 mode selection and the dispersion relation
2.7 pattern generation with single-species models�� spatialheterogeneity with the spruce budworm model
2.8 spatial patterns in scalar population interaction diffusionequations 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 ofreactiondiffusion mechanisms
3.1 mammalian coat patterns--'how the leopard got its spots'
3.2 teratologies�� examples of animal coat patternabnormalities
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 andsnakes
4. i stripe pattern formation in the alligator�� experiments
4.2 modelling concepts�� determining the time of stripeformation
4.3 stripes and shadow stripes on the alligator
4.4 spatial patterning of teeth primordia in thealligator��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 celi-chemotaxissystem

5. bacterial patterns and chemotaxis
5.1 background and experimental results
5.2 model mechanism for e. coli in the semi-solid experiments
5.3 liquid phase model�� intuitive analysis of patternformation
5.4 interpretation of the analytical results and numericalsolutions
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, basic patterns
5.9 numerical results with initial conditions from theexperiments
5.10 swarm ring patterns with the semi-solid phase modelmechanism
5.11 branching patterns in bacillus subtilis

6. mechanical theory for generating pattern and form indevelopment
6.1 introduction, motivation and background biology
6.2 mechanical model for mesenchymal morphogenesis
6.3 linear analysis, dispersion relation and pattern formationpotential
6.4 simple mechanical models which generate spatial patterns withcomplex dispersion relations
6.5 periodic patterns of feather germs
6.6 cartilage condensation in limb morphogenesis and morphogeneticrules
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

7. evolution, morphogenetic laws, developmental constraints andteratologies
7.1 evolution and morphogenesis
7.2 evolution and morphogenetic rules in cartilage formation in thevertebrate limb
7.3 teratologies ��monsters��
7.4 developmental constraints, morphogenetic rules and theconsequences for evolution

8.a mechanical theory of vascular network formation
8.1 biological background and motivation
8.2 cell-extracellular matrix interactions for vasculogenesis
8.3 parameter values
8.4 analysis of the model equations
8.5 network patterns�� numerical simulations and conclusions

9. epidermal wound healing
9.1 brief history of wound healing
9.2 biological background�� epidermal wounds
9.3 model for epidermal wound healing
9.4 nondimensional form, linear stability and parametervalues
9.5 numerical solution for the epidermal wound repair model
9.6 travelling wave solutions for the epidermal model
9.7 clinical implications of the epidermal wound model
9.8 mechanisms of epidermal repair in embryos
9.9 actin alignment in embryonic wounds�� a mechanical model
9.10 mechanical model with stress alignment of the actin filamentsin two dimensions

10. dermal wound healing
10.1 background and motivation---general and biological
10.2 logic of wound healing and initial models
10.3 brief review of subsequent developments
10.4 model for fibroblast-driven wound healing�� residual strain andtissue remodelling
10.5 solutions of the model equation solutions and comparison withexperiment
10.6 wound healing model of cook ��1995��
10.7 matrix secretion and degradation
10.8 cell movement in an oriented environment
10.9 model system for dermal wound healing with tissuestructure
10.10 one-dimensional model for the structure of pathologicalscars
10.11 open problems in wound healing
10.12 concluding remarks on wound healing

11. growth and control of brain tumours
11.1 medical background
11.2 basic mathematical model of glioma growth and invasion
11.3 tumour spread in vitro�� parameter estimation
11.4 tumour invasion in the rat brain
11.5 tumour invasion in the human brain
11.6 modelling treatment scenarios�� general comments
11.7 modelling tumour resection ��removal�� in homogeneoustissue
11.8 analytical solution for tumour recurrence afterresection
11.9 modelling surgical resection with brain tissueheterogeneity
11.10 modelling the effect of chemotherapy on tumour growth
11.11 modeling tumour polyclonality and cell mutation

12. neural models of pattern formation
12.1 spatial patterning in neural firing with a simpleactivation-inhibition model
12.2 a mcchanism for stripe formation in the visual cortex
12.3 a model for the brain mechanism underlying visualhallucination patterns
12.4 neural activity model for shell patterns
12.5 shamanism and rock art

13. geographic spread and control of epidemics
13.1 simple model for the spatial spread of an epidemic
13.2 spread of the black death in europe 1347-1350
13.3 brief history of rabies�� facts and myths
13.4 the spatial spread of rabies among foxes i�� background andsimple model
13.5 spatial spread of rabies among foxes ii��three-species ��sir��model
13.6 control strategy based on wave propagation into a non-epidemicregion�� estimate of width of a rabies barrier
13.7 analytic approximation for the width of the rabies controlbreak
13.8 two-dimensional epizootic fronts and effects ot variable foxdensitics�� quantitative predictions for a rabies outbreak inengland
13.9 effect of fox immunity on spatial spread of rabies

14. wolf territoriality, wolf-deer interaction and survival
14.1 introduction and wolf ecology
14.2 models for wolf pack territory formation�� single pack--homerange model
14.3 multi-wolf pack territorial model
14.4 wolf-deer predator-prey model
14.5 concluding remarks on-wolf territoriality and deersurvival
14.6 coyote home range patterns
14.7 chippewa and sioux intertribal conflict c1750-1850
appendix
a. general results for the laplacian operator in boundeddomains
bibliography
index