Fractals and Chaos Simplified for the Life Sciences

[Cover] [Abbreviated Contents] [Contents] [Index]

Page 261
dimension (see chaos, phase space, dimension)
introduction (Part 2, Chapter 1) 115-127
phase space (Part 2, Chapter 2) 129-153
biological implications 152
construction 122, 123, 130, 131, 138, 139, 142, 143
definition 130
deterministic vs. random 122, 126, 134-137, 142, 148
dimension 122, 126, 134-137, 142, 150, 192
electrocardiogram 196, 197
electroencephalogram 198, 199
epidemics 194, 195
hair cells 140, 141
heart cells 144-147
logistic equation 122, 126, 134
Lorenz equation 131, 132, 134, 158, 166
overview of the phase space analysis 148, 149
problems with the phase space analysis 206-217, 222
random mechanism 122, 126, 136
vectors 218, 219
problems with the chaos analysis
amount of data 210
embedding theorems 214
interpretation of low dimensional attractor 216
lag 212
summary 208
properties 124, 126, 238
references, suggested 240, 241
sensitivity to initial conditions (Part 2, Chapter 3) 155-173
biological implications 172
definition 162
Lorenz equations 156-161, 166, 167
Poincaré 164
time series 160, 161
strange 166-169
summary 238
chaotic universe 164
characteristic scale 6
checkerboard 80, 81
chemical reactions 40, 68, 180-185
chickenpox 194, 195
Churilla 17
clockwork universe 164
coastline 32, 33
Cohen 197, 203
coin games
ordinary coin toss 78
St. Petersburg Game 78
complex output 120, 124
construction of the phase space set 122, 130, 138, 142
control of chaos (see chaos, control)
convection 156
convulsions 198
cornea 68
correlations 70, 220
Coulson 95
coupled maps 248, 249
covering dimension 47, 60, 61
Creutzfeld-Jakob 199
Creutz 249
cultured cells 14-17, 22, 144-147
Czegledy 67
D
Daccord 15
data (see time series)
definitions
bifurcation 176
chaos 118, 124, 168
control of chaos 226

 
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