生物数学-第1卷-第3版

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