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 pattern
abnormalities
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 and
snakes
4. i stripe pattern formation in the alligator： experiments
4.2 modelling concepts： determining the time of stripe
formation
4.3 stripes and shadow stripes on the alligator
4.4 spatial patterning of teeth primordia in the
alligator：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-chemotaxis
system
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 pattern
formation
5.4 interpretation of the analytical results and numerical
solutions
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 the
experiments
5.10 swarm ring patterns with the semi-solid phase model
mechanism
5.11 branching patterns in bacillus subtilis
6. mechanical theory for generating pattern and form in
development
6.1 introduction, motivation and background biology
6.2 mechanical model for mesenchymal morphogenesis
6.3 linear analysis, dispersion relation and pattern formation
potential
6.4 simple mechanical models which generate spatial patterns with
complex dispersion relations
6.5 periodic patterns of feather germs
6.6 cartilage condensation in limb morphogenesis and morphogenetic
rules
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 and
teratologies
7.1 evolution and morphogenesis
7.2 evolution and morphogenetic rules in cartilage formation in the
vertebrate limb
7.3 teratologies （monsters）
7.4 developmental constraints, morphogenetic rules and the
consequences 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 parameter
values
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 filaments
in 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 and
tissue remodelling
10.5 solutions of the model equation solutions and comparison with
experiment
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 tissue
structure
10.10 one-dimensional model for the structure of pathological
scars
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 homogeneous
tissue
11.8 analytical solution for tumour recurrence after
resection
11.9 modelling surgical resection with brain tissue
heterogeneity
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 simple
activation-inhibition model
12.2 a mcchanism for stripe formation in the visual cortex
12.3 a model for the brain mechanism underlying visual
hallucination 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 and
simple 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-epidemic
region： estimate of width of a rabies barrier
13.7 analytic approximation for the width of the rabies control
break
13.8 two-dimensional epizootic fronts and effects ot variable fox
densitics： quantitative predictions for a rabies outbreak in
england
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--home
range model
14.3 multi-wolf pack territorial model
14.4 wolf-deer predator-prey model
14.5 concluding remarks on-wolf territoriality and deer
survival
14.6 coyote home range patterns
14.7 chippewa and sioux intertribal conflict c1750-1850
appendix
a. general results for the laplacian operator in bounded
domains
bibliography
index
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