Murray J.D. Mathematical Biology: I. An Introduction
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Index
Activation, 201
waves, 467
Activator, 175, 197, 206
Activator–inhibitor
kinetics, 206
mechanism, 206, 216, 255
parameter space for periodic solutions, 255
Age dependent model
epidemic, 361
population, 36
similarity solution, 39, 40
threshold, 39
Age-structured model
alligator, 123
Aging, 44
AIDS (acquired immune deficiency syndrome),
316, 327
AZT, 333
clinical categories, 335
haemophiliacs, 394
homosexual epidemic model, 338
myths, 333
periodic outbreak, 339
protease inhibitor, 342
Scientific American Special Report, 334
statistics, 333
UNAIDS report 1997, 334
AIDS (autoimmune deficiency syndrome),
333
Aikman, D., 403
Allee effect, 71, 106, 108
Alligator mississippiensis (see Alligators)
Alligators
carrying capacity, 129
clutch size, 139
egg incubation temperature, 121
environmental fluctuations, 136
extinction, 129
hatchling survival, 139
Louisiana, 121
maternity function, 132
nesting regions, 121, 124
net reproductive rate, 135, 138
relative fitness, 122, 125
sex, 120
sex ratio, 125, 138, 139
stable age distributions, 137
survivorship, 133, 138
three-region model, 124
U.S. distribution, 130
Allosteric
effect, 197
enzyme, 215
Alpert, M., 143
Alt, W., 406
Ammerman, A.J., 444
Amphibian eggs, 464
calcium waves, 467
Anderson, R.A., 253
Anderson, R.M., 318, 337, 340
Andrews, H.V., 144
Animal dispersal model, 402
Animal pole, 468
Anorexia, 147
Antichaos, 75
Antzelevitch, C., 278, 291, 292
Aoki, K., 444
Aperiodic solutions (discrete models),
56
Aphid (Aphidicus zbeckistanicus), 88
Aplysia, 288
Arnold, R., 440
Aronson, D.G., 452, 453
Aubin, J.-P., 75
Avnir, D., 485
AZT, 333
Bacchetti, P., 392
Backcalculation, 392
Bacterial inflammation, 406
Baders
MAFF report, 369
537
538 Index
Badgers
criss-cross model, 370
spatial spread, 390
Tb parameters, 375
tuberculosis, 369
control programme cost, 387
Bailey, N.J.H., 319
Baleen whale model, 41
Bar-Eli, K., 233
Barkley, D., 276
Bassingthwaighte, J.B., 484, 499
Beck, M.T., 418
Beddington, J.R., 30, 33, 109, 113, 114
Behaviour (marital interaction)
influenced, 151
uninfluenced, 151
Belousov, B.P., 220, 257
Belousov–Zhabotinskii (BZ) reaction, 257
analytical approximation for period of
oscillation, 275
basic mechanism, 258
bursting, 276
chaotic behaviour, 276
coupled systems, 294
determinsitic chaos, 276
Field–K
¨
or
¨
os–Noyes model, 257
hysteresis, 276
kinematic waves, 418, 450
oscillations, 220
periodic-chaotic sequences, 276
relaxation oscillator, 268
Benchetrit, G., 26, 75
Benedict, L.M., 75
Benoit, E., 233
Bentil, D.E., 370, 374, 375, 377, 379
Benton, M.J., 119
Berding, C., 351–354, 360
Bernoulli, D., 318, 361
Best, E.N., 278, 289–291
Bifurcating periodic solution, 28
Bifurcation
period-doubling, 52, 55
pitchfork, 52
tangent, 51, 56
Bilharzia (schistosomiasis), 104, 329
Binomial distribution, 396
Biochemical reactions, 175
Biological clock, 219
fruit fly, 279
Biological oscillator, 218, 226
black holes, 288
breathing, 218
emergence of fruit flies, 218
emission of cAMP (Dictyostelium cells), 219
general results, 226
λ − ω system, 238
Lotka, 203
neural activity, 218
parameter domain determination, 234, 235
two-species models, 234
Biological pest control, 114
Biological switch, 207, 216, 218, 226, 230, 276
general results, 226
Biological time
geometric theory, 278
Biomass, 101
Bistability, 212
Black holes (in oscillators), 278, 314
cardiac oscillations, 291
real biological oscillator, 288
singularity, 286, 289
Bombykol, 405
Bombyx mori (silk moth), 405
Boons, M.C., 11
Borghans, J.A.M., 181
Bovine spongiform encephalopathy (BSE), 391
Bovine tuberculosis, 369
cellular automaton control model, 385
control programme, 384
control strategies, 379
criss-cross model, 370
critical value for herd immunity, 383
eradication campaign, 379
herd immunity, 383
immunization model, 379
mortality, 371
preferred vaccination policy, 385
risk factor, 385
spatial spread, 390
Brauer, F., 33
Bray, W.C., 219
Breathing, 278
synchrony, 278
Britton, N.F., 401, 437
Brøns, M., 233
Brown, J.A., 375
Brusselator (reaction diffusion), 253
BSE, 391
human Creutzfeldt–Jacob disease, 391
Bubonic plague, 326
Buchanan, J.T., 424, 430
Buck, E., 296
Buck, J., 296
Budworm (spruce)
model, 7, 40
outbreak spread, 464
travelling waves, 460
Bull, J., 121, 122
Bunting, P.S., 175
Burger, M., 220, 257, 276
Index 539
Burke, M.A., 188, 196, 197
Bursting (periodic), 232
Belousov–Zhabotinskii reaction, 276
Bustard, H.R., 129
Butterworth, A.E., 360
Cahn, J.W., 415
Calcium-stimulated-calcium-release mechansim,
464
Calcium waves on amphibian eggs, 467
California sea otter reinvasion, 478
Camazine, S., 47
cAMP signal transduction, 219
Canard, 233
Cancer, 44
breast, 252
prostrate, 219, 244
Canosa, J., 444, 447
Capasso, V., 318
Carbon monoxide poisoning, 401
Cardiac
arrhythmias, 278, 293
black holes, 293
death, 278, 291
failure, 293
oscillator, 291
pacemaker cells (periodic beating), 291
Cardiac fibrillation, 75
Carelli, V., 252
Carroll, R.H., 119
Cartwright, M., 245, 246, 252
Caserta, F., 499
Castration, 252
chemical, 245, 252
Depo-provera, 245
drug induced, 245
Lupron, 245
Caswell, H., 46
Catastrophe
cusp, 10
Nile perch (Lake Victoria), 104
in perception, 11
Cattle, criss-cross model, 370
Cavali-Sforza, L.L., 444
Cell
energy approach to diffusion, 413
energy density concept, 414
potential, 413
Central pattern generator, 418, 422
Chabreck, R.H., 122
Chaos, 28, 58, 59, 62, 233
Belousov–Zhabotinskii (BZ) reaction, 276
brain activity, 75
data, 66
determinstic chaos in BZ reaction, 276
epilepsy, 75
theory, 58
Chaotic
mask, 62
solutions, 56, 59
Characteristic polynomial, 507
Charlesworth, B., 36
Charnov, E.L., 121, 122
Cheer, A., 465, 468, 469, 471
Chemoreceptors, 22
Chemotaxis, 395, 405
blow-up, 408
equations, 407
flux, 406
index, 408
induced movement (cells), 406
log law, 408
reaction-diffusion system, 407
receptor law, 408
Cheyne–Stokes disease, 21
Cheyne–Stokes respiration
delay model, 21
periodic oscillations, 26
Chiang, H.C., 404
Chlamydia (venereal disease), 327
Cholera epidemic, 318
Clark, C.W., 30, 35, 65, 67
Clerk Maxwell, James, 409
Cobwebbing (discrete models), 52
Coding
Cumulative RCISS, 149
Facial Action System, 150
MICS, 169
RCISS, 148
SPAFF, 172
Cohen, A.H., 422–424, 430, 436
Cohen, D.S., 413, 416
Cohen, Y., 67
Colbert, E.H., 119
Cole, J.D., 444
Cole, L.C., 133
Community matrix (population), 82
Competition, 79
models, 94
population, 79
spatial, 99
Confined set, 92
Conservative system (population), 80
Contraception, male, 244
Contraction waves, 469
Control, 114
Control system (biological), 221
Convection, 449
nonlinear, 454
Cook, J., 67, 146, 471, 478, 480
540 Index
Cooperativity (reaction kinetics), 197, 224
Cordella, L., 288
Cosivi, O., 334
Cosnard, M., 75
Cotton, D.W.K., 44, 67, 72, 75
Couder, Y., 48
Couple (married)
avoiders, 150
conflict–avoiding, 151
hostile, 150
hostile-detached, 150
influenced steady state, 157
newlywed, 174
null cline, 156
parenthood, 174
regulated, 148
stability, 156
stable, 150
steady state, 156
unregulated, 148
unstable, 150
validators, 150
volatiles, 150
Coupled oscillators, 278
model system, 293
Crank, J., 398
Creutzfeldt–Jacob (CJ) disease, 391
Crews, D., 121
Criss-cross
disease, 328
epidemic threshold, 330
SI (epidemic) model, 329
Crocodiles
birth rate, 135
death rate, 135
life history tactics, 141
population stability, 123
world distribution, 130
Cross, S.S., 44, 67, 72, 75, 487
Cusp catastrophe
in perception, 11
Cvitanovi
´
c, P., 62
Dallon, R., 233, 406
De Boer, R.J., 180
DeBach, P., 115
Decroly, O., 233
Deeming, C., 121, 122, 142
Delay models
physiological diseases, 21
testosterone control, 245
Delay population model, 13
critical delay, 19
linear analysis, 17
periodic solution, 15, 17, 19
Dembo, M., 401
Demongeot, J., 75
Descartes’ rule of signs, 509
Dictyostelium discoideum, 406, 437
cell division, 219
kinetics models, 406
periodic emission, of cAMP, 219, 233
wave phenomena, 219
Diekmann, O., 36, 319, 322
Dietz, D.C., 123
Dietz, K., 328, 361, 378
Diffusion, 395
cell potential, 413
density dependent diffusion model for insect
dispersal, 417
energy approach, 413
facilitated, 401
Fickian, 397, 408
flux, 397
local, 408
long range, 408
rotational, 401
short range, 408
variable, 471
Diffusion coefficient, 397
biochemicals, 438
haemoglobin, 397
insect dispersal, 438
oxygen (in blood), 397
Diffusion equation
density dependent diffusion, 402
random walk derivation, 395
scalar, 416, 438
Diffusion limited aggregation, 498
Dioxin, 143
Discrete delay (population) models, 62
characteristic equation, 63, 66
crash-back, 70
extinction, 71
Discrete population models
aperiodic solutions, 56
chaotic solutions, 53, 59
cobweb solution procedure, 49
critical bifurcation parameter, 51
density-dependent predator–prey, 113
eigenvalue, 50
extinction, 71
graphical solution procedure, 49
harvesting, 78
m-periodic solutions, 61
maximum population, 70
minimum population, 70
odd periodic solutions, 56
orbit, 61
oscillations, 51
Index 541
parasite epidemic, 118
period-doubling bifurcation, 52
periodic doubling, 55
periodic solutions, 54, 59
predator–prey, 109
single species, 44
stability, 59
stability analysis, 62
tangent bifurcation, 51, 56
trajectory, 61
Disease
criss-cross, 328
incubation period, 327
new, 335
Dispersion relation, 442, 456
long range diffusion, 410
Dispersive variability, 471
Distribution, bionomial, 396
DLA (diffusion limited aggregation), 498
DNA (deoxyribonucleic acid), 221
Dogfish, 422
Domain of attraction, 97
Donnelly, C.A., 392
Douady, S., 48
Driver, R.D., 20
Drosophila melanogaster, 278. See also fruit fly
Drug
epidemic critical population, 369
epidemic infectiousness, 368
epidemic model, 366
response, 366, 367
Duesberg, P., 333
Duffy, P., 392
Dynamic diseases (physiological), 21
Earn, D.J.D., 393
Ecological
Allee effect, 71
caveats (modelling), 69
extinction, 64, 70, 71
predation pit, 71
sterile insect control, 77
Ecological invasion with few disperers, 480
Edblom, E.C., 233
Edelstein-Keshet, L., 1, 405
Ekman, P., 150
Electric potential, 425
Elton, C.S., 36, 84, 478
Embryonic heart cells, 295
Emotional inertia, 169
Environmental sex determination (ESD), 120
Enzyme, 175
basic reaction, 175
conservation, 176
kinetics, 175
substrate complex, 175
substrate reaction, 175
suicide, 188
EOB reaction, 233
Epidemic
age dependent model, 361
age dependent threshold, 362
basic AIDS model, 338
Bombay plague, 325
contact rate, 321
drug infectiousness, 368
drug use, 365
drug user’s response, 368
history, 315
influenza, 326
modelling goals, 360
models, 319
oscillatory behaviour, 327
plague, 326
relative removal rate, 321
reproduction rate, 322
SEIR model, 393
severity, 323
survival, 364
threshold, 321, 361
threshold analysis, 365
Epilepsy, 75
Epileptic seizure, 75
Epstein, I.R., 233
Ermentrout, G.B., 296, 299, 429
Essunger, P., 336
Euler, L., 136
Exact solutions, 449
cubic polynomial, 507
Excitable kinetics
caricature, 466
model, 465
wave, 464
Falconer, K.J., 485
Famiglietti, E.V., 485
Feedback
control, 201, 221, 254
inhibition, 203, 222
negative, 222, 254
positive, 222, 254
Feedback mechanisms, 35, 201, 221, 222
conditions for limit cycle solutions, 224
confined set, 223
frequency of oscillation, 225
testosterone control, 245
Feigenbaum, M.J., 58
Female determining factor (FDF), 143
Ferguson, M.W.J., 121, 122, 124, 133, 142
Ferguson, N.M., 392
542 Index
Ferri
`
ere, R., 103
Ferro, V.A., 252, 253
Fertility, poisons, 143
Feshbach, H., 408
Fibonacci, 45
angle, 46
sequence, 45
Fibrillation (cardiac), 293
spiral waves, 293
Fictive swimming, 422
Field, R.J., 220, 257–261, 276
Field–K
¨
or
¨
os–Noyes (FKN) model for the BZ
reaction, 258, 259
comparison with experiment, 268
confined set, 265
limit cycle solution, 261
linear stability analysis, 261
nondimensionalisation, 260
nonlocal stability, 265
periodic oscillations, 263
relaxation model for limit cycle, 271
reversibility, 276
Fife, P.C., 437, 461
Fincham, F.D., 173
Firing threshold, 470
Fisher, G.H., 11
Fisher, R.A., 122, 400, 440
Fisher–Kolmogoroff equation, 400,
439
asymptotic solution, 444
axisymmetric, 443
exact solution, 444, 446
initial conditions, 442
wave solution, 440
Fishery management
economic return, 69
model (discrete), 67
optimisation problem, 67
stabilising effect, 69
strategy, 67
Fitzhugh, R., 239
FitzHugh–Nagumo model, 239, 240, 242,
278, 289
conditions for limit cycles, 243
piecewise linear model, 243
space clamped model, 256
Flores, J.C., 99, 115
Fossils, living, 119
Foster, K.R., 316
Fowler, A.C., 11, 26
Fox, J.P., 383
Fractal dimension, 490
Hausdorf, 496
practical determination, 492
von Koch curve, 492
Fractals, 484
abuse, 484
biological examples, 485
box counting, 495
definition, 492
dimension calculation, 490
examples, 487
generation, 487
microscopy, 487
pulmonary blood flow, 486
nonlinear, 489
non self-similar, 495
pulmonary vascular tree, 486
scaling laws, 491
self-similar, 489, 491
Sierpinski, 488
space filling, 496
von Koch curve, 487
Freed, M.A., 485, 486
Frenzen, C.L., 72, 181
Frerichs, R.R., 385
Friedlander, M.J., 485
Friesen, W,V., 150
Frost, S.D.W., 336
Fruit fly (Drosophila melanogaster),
278
biological clock, 279
emergence (eclosion), 279
G
´
asp
´
ar, V., 233
Galvanotaxis, 408
flux, 408
Ganapathisubramanian, N., 212–215
Gans, C., 119, 123
Garrett, L., 317, 335
Gaston, J., 489
Gatto, M., 103
Gaussian (normal) probability distribution,
396
Genetic sex determination (GSD), 120
Genetics, 44
Georges, A., 142
Getz, W.M., 35, 65, 67
Gibbs, R.J., 455
Gierer, A., 206
Gilkey, J.C., 468, 469
Gilpin, M.E., 83, 84
Glass, L., 21, 22, 24, 26, 27, 295
Glenny, R.W., 486
Glycolysis, 218
Goh, B.-S., 67
Goldberger, A.L., 44
Goldbeter, A., 219, 233, 257, 406
Golden mean, 46
Goldstein, S., 454
Index 543
Gonorrhea, 327
control, 331
multi-group model, 331
Goodwin, B.C., 221
Goodwin, T.M., 123
Goselerin (drug), 244
Gottman, J.M., 67, 146–150, 173,
174
Gottman–Levenson variable, 148
Grasshopper dispersal, 403
Gray, P., 210, 212
Griffith, J.S., 222
Grillner, S., 422
Grindrod, P., 437
Gros, G., 401
Growth rate effect of sex ratio, 143
Guckenheimer, J., 429, 501
Guevara, M.R., 295
Gumowski, I., 62
Gurney, W.S.C., 16, 88, 136
Gurtin, M.E., 123
Guttman, R., 288, 291
Gutzke, W.H.N., 121
Gy
¨
orgyi, L., 276
Hadeler, K.P., 328
Haematopoiesis, 26
Haemoglobin, 175, 197, 401
Haight, R.G., 35, 65, 67
Hall, P.A., 44
Hancox, M., 391
Hanson, F.E., 296, 297
Hanusse, S.P., 234, 260
Harris-Warrick, R.M., 422
Harvesting strategy, 33
Hassell, D.C., 11
Hassell, M.P., 44, 71, 109
Hastings, A., 1
Hastings, S.P., 265
Heesterbeek, J.A.P., 319
Heligmosoides polygyrus, 352
Herd immunity, 322
Herz, V.M., 350
Hethcote, H.W., 327, 328, 332, 381
Hewitt, G., 403
Hilbert, H., 497
Hilborn, R., 35, 67
Hill
coefficient, 22, 222
equation, 201
function, 22
plot, 201
Hilliard, J.E., 415
Hines, T.C., 123
Hippocrates, 316
HIV (human immunodeficiency virus)
biological background, 335
cocktail drug therapy, 343
critical drug efficacies, 349
delay model, 350
delay model with therapy, 350
doubling time, 340
drug therapy, 341
infection time course, 336
new cases, 334
parameter estimates, 344
reverse transcriptase inhibitors, 343
T-cell recovery, 344
T-cells, 335
therapy, 347
time lag model, 350
transmission dynamics, 333
viral production, 342
Ho, D.D., 335, 337, 341, 344
Hodgkin, A.L., 218, 239, 240, 289,
290
Hodgkin–Huxley
FitzHugh–Nagumo model, 239, 242
perturbed oscillations, 289
piecewise linear model, 243
space-clamped dynamics, 239
system excitability, 240
theory of nerve membranes, 239
Holden, A.V., 62, 103
Holladay, A.J., 315
Holmes, P.J., 429, 501
Hookworm, 351
Hooper, E., 333
Hopf
bifurcation theorem, 220
limit cycles, 220
Hopf, L., 408
Hoppensteadt, F.C., 1, 26, 44, 62, 123, 278,
327, 361, 365
Hormone, 244
Hosono, Y., 459
Howard, L.N., 220, 418, 419, 421
Howe, A.H., 316
Hsu, S.-B., 94
Huberman, B.A., 415
Hudson Bay Company, 36
Huffaker, A.F., 115
Hunding, A., 224
Husain, M.A., 245, 246, 252
Huxley, A.F., 218, 239, 240, 289, 290
Hydra attenuata, 288
Hyman, J.M., 62
Hypothalamus, 245
Hysteresis, 8, 209
in perception, 11
544 Index
Iasemidis, L.D., 75
Inertia parameter, 154, 167
Infectious diseases, control, 318
Influence function, 151, 155
Inhibition, 201
Inhibitor, 175, 198, 206
Insect
aggregation, 405
control, 114, 460
density dependent diffusion dispersal model,
402, 416
dispersal model, 402
infestation break, 464
outbreak, 7
population spread, 460
refuge, 460
swarm, 405
Insect dispersal
variable diffusion, 471
Interacting populations
characteristic polynomial (discrete model),
30
community matrix, 82
competition, 79, 402
complexity and stability, 83
continuous models, 79
density-dependent predator–prey (discrete),
113
discrete growth models, 109
Lotka–Volterra, 79
lynx-snowshoe hare, 83
mutualism, 79
predator–prey, 79
Interaction
family, 146
social, 146
International Whaling Commission (IWC), 41
Invasion
establishment phase, 481
lag period, 481
Iodate–arsenous acid reaction, 212
Isham, V., 337
Isolas, 208–210, 212
J
¨
ager, W., 408
Jacob, C., 75
Jacob, F., 221
Jalife, J., 278, 291, 292
James, W.H., 143
Joanen, T, 121, 122–124, 129
Johnson, S.D., 143
Johnston, C.M., 142, 143
Jordan, D.W., 20, 505
Julia sets, 489
Jury conditions, 507
Kaandorp, J.A., 485
Kalamangalam, G.P., 26
Kao, R.R., 390
Kareiva, P., 402, 438
Kashin, S., 422
Kath, W.L., 465
Kawasaki, K., 402, 403, 405, 471, 478
Keener, J.P., 21, 218, 232, 239, 295
Keller, E.V., 407
Keller, K.H., 406
Kermack, W.O., 318, 320, 325
Kernel
biharmonic contribution, 412
excitatory-inhibitory, 411, 412
moments, 412
Kevorkian, J., 37, 39, 444, 454
Keyfitz, N., 133
Keymer, A.E., 352
Kinematic waves, 418
Kinetics, 175
Kingsland, S.E., 1, 3
Kirschner, D.E., 336, 344
Kolmogorov equations, 101
Kolmogorov, A., 101, 400, 440, 442
Kopell, N., 418, 419, 421, 422, 424, 430
K
¨
or
¨
os, E., 259
Kostova, T.V., 137
Kot, M., 1, 30, 36, 44, 48, 71, 79, 103, 114, 402,
471
Krebs, C.J., 17
Krinsky (Krinskii), V.I., 278
Krokoff, L.J., 148
Kunz, M., 47
Lai, H., 328
Laidler, K.J., 175
Lajmanovich, A., 331
Lake Victoria Nile perch catastrophe,
104
λ − ω systems, 238
complex form, 238
oscillator, 238
Lamprey, 418, 422
Lane, D.C., 465, 468, 469, 471
Lang, J.W., 123, 142, 144
Lara-Ochoa, F., 416
Larson, D.A., 443, 448
Larter, R., 75
Latis niloticus (Nile perch), 104
Lauffenburger, D.A., 406, 408
Lauritsen, J., 333
Lauwerier, H.A., 109
Law of Mass Action, 176
Lefever, R., 253
Leigh, E., 83
Index 545
Lemming, 16
Leonardo of Pisa, 45
Lesbianism, 143
Leslie matrix, 36, 46
Leslie, P.H., 36
Leukaemia, 28
Leukocyte cells, 406
Levenson, R.W., 147, 149
Levin, S.A., 35, 67, 88, 478
Levinson, D.A., 44
Lewis, E.R., 508, 509
Lewis, M.A., 402, 480
LH (luteinising hormone), 245
LHRH (luteinising hormone releasing hormone),
245
Li, T.-Y., 56, 59
Liapunov function
delay equation, 20
Limit cycle, 15
analysis of BZ relaxation oscillation model, 220
conditions for FKN model (BZ reaction), 261
coupled, 293
feedback control mechanisms, 224
FitzHugh–Nagumo model, 240
λ − ω system, 238
period (delay model), 20
phase locking, 293, 424
predator–prey model, 93
simple example, 280
‘simplest’ kinetics, 234
tri-molecular reaction, 234
Linnaeus, 120
Lipsitz, L.A., 44
Logical parameter search (LPS), 375
Logistic
discrete model, 49, 76
growth, 3
Long range (lateral)
diffusion, 408
integral formulation, 410
kernel function, 411
Lorenz equations, 103
Lorenz, E.N., 58, 103, 265
Lotka reaction mechanism, 203
Lotka, A.J., 79, 80, 123, 203
Lotka–Volterra, 79
competition model, 94
multi-species model, 83
predator–prey model, 79
Lubina, J.A., 478
Lubkin, S.R., 369
Lucila cuprina (sheep-blowfly), 15, 16
Luckhaus, S., 408
Ludwig, D., 7, 35
Luteinizing hormone (LH), 245
Luteinizing hormone releasing hormone (LHRH),
245
Luther, R.-L., 440
Lynx-snowshoe hare interaction, 83
m-periodic solutions, discrete population models,
61
MacCamy, R.C., 123
Macdonald, D., 370
MacDonald, N., 20, 224
Mackey, M.C., 21, 22, 24, 26, 27, 295
Maini P.K., 181
Malaria, 328
Male determining factor (MFD), 142
Malthus, T.R., 2
Mandelbrot, B.B., 109
Mangel, M., 30, 35, 67
Manoranjan, V.S., 443
Marek, M., 293, 294, 313
Marion, W.R., 123
Marital
dissolution, 147
inertia, 167
steady states, 167
Marital classification, 167
Marital dissolution, 168
mechanism, 172
Marital interaction, 44
basin of attraction, 157
emotional inertia, 169
influence components, 154
influence function, 151
stability condition, 160
uninfluenced steady state, 154
Marital interaction model
inertia, 154
intervention effects, 172
practical benefits, 170
predictions, 172
test, 172
Marital modelling strategy, 153
Marital therapy, 163
Marital topology, 150
Marriage, 44
Avoiding, 166
classification, 167
hostile, 166
Hostile-detached, 166
physiological arousal, 172
postive effect, 150
repair, 170, 173
stable, 164
unstable, 166
Validating, 166
Volatile, 166