|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Marotto F. — Introduction to Mathematical Modeling Using Discrete Dynamical Systems |
|
|
|
| Предметный указатель |
Absolute error 137 138
Air-resistance 4 19 133 140
Alternating series 32
Amortized loan 60
Annuity Savings Formula 59
Annuity Savings Model 22
Annuity, ordinary 21 22 58
Approximate solution, differential equation(s) 134
Approximate solution, differential equation(s), system of 275 302
Approximate solution, root of equation 127—133 154 175 314
Asymptotic behavior/dynamics 17 69 see
Attractor 106 see
Attractor, sink 205 271
Attractor, strange 186 296 305
Autonomous differential equation(s) 136
Autonomous differential equation(s), fixed point 137
Autonomous differential equation(s), system of 275 301 302
Autonomous linear equation 28 30
Autonomous linear equation, fixed point 71
Autonomous linear equation, oscillation 73
Autonomous linear equation, solution, homogeneous 43
Autonomous linear equation, solution, non-homogeneous 53 54
Autonomous linear equation, stability 72
Autonomous linear system see "Linear system"
Autonomous nonlinear equation see "Nonlinear equation"
Autonomous nonlinear system see "Nonlinear system"
Barnsley fern 309
Barnsley, M. 308
Basin of attraction 106 121 177 179 314
Bifurcation, nonlinear equation, fixed point 166
Bifurcation, nonlinear equation, n-cycle 171
Bifurcation, nonlinear equation, period-doubling cascade 171—173
Bifurcation, nonlinear system, fixed point 290—294
Bifurcation, nonlinear system, Hopf 291
Bifurcation, nonlinear system, irrationally periodic cycle 292
Bifurcation, nonlinear system, m-cycle 293 294
Bifurcation, nonlinear system, period-doubling cascade 290 291
Bifurcation, nonlinear system, period-multiplying cascade 293—295
Birth rate 23 24
Bouncing ball 6—9
Bouncing ball model 9
Box-Counting Dimension 309—311
Butterfly effect 180
Cantor set 303 304 311
Carrying capacity 89 267 268
Change of variable 55 74 155 255
Chaos 173 176 186
Chaos, nonlinear equation 176—186
Chaos, nonlinear equation, butterfly effect 180
Chaos, nonlinear equation, dense orbit 178
Chaos, nonlinear equation, homoclinic orbit 185
Chaos, nonlinear equation, horseshoe 183
Chaos, nonlinear equation, infinite periodic cycles 177
Chaos, nonlinear equation, Lyapunov exponent 180—182
Chaos, nonlinear equation, period three 184
Chaos, nonlinear equation, scrambled set 176 177
Chaos, nonlinear equation, sensitive dependence 179 180
Chaos, nonlinear equation, snap-back repeller 185
Chaos, nonlinear equation, transitive function 178
Chaos, nonlinear system 295—299
Chaos, nonlinear system, homoclinic orbit 298 299
Chaos, nonlinear system, horseshoe 296—298
Chaos, nonlinear system, snap-back repeller 289 290
Chaos, nonlinear system, strange attractor 296
Chronic illness 260
Cobweb graph 110—114
Cobweb graph and nonlinear dynamics, chaos 179 183 185
Cobweb graph and nonlinear dynamics, fixed point 119
Cobweb graph and nonlinear dynamics, periodic cycle 145 149 150
Cobweb graph and time series graph 111 113 114
Coefficient matrix, linear system 219 255
Coefficient matrix, linear system, eigenvalues see "Eigenvalue(s)"
Coefficient matrix, linear system, eigenvectors 220—225
Coefficient matrix, simultaneous equations 214—216
coin toss 3 4
Competing species 191 267
Competing species, Linear Competition Model I/II 191 192
Competing species, Nonlinear Competition Model 267
Complex conjugate 239
Complex eigenvalue(s) see "Eigenvalue(s)"
Complex number 238
Complex plane 240
Composition (notation) 147 283
Compound interest 13 14 21 22 58—61
Compound interest formula 14 43
Compound Interest Model 13
Compound interest, exponential growth of 45
Computer graphics/animation 194 196 207 302 309
Computer software 33
Computer software, Mathematica 320—326
Computer software, Microsoft Excel 315—320
Conjugate, complex 239
Contagious Disease 90 91 268 269
Contagious Disease, infection rate 90 99 167 268 269 288
Contagious Disease, Nonlinear Infection Model I/II 91
Contagious Disease, Nonlinear Infection-Recovery Model 269
Contagious Disease, recovery rate 90 268 269
Contamination 27 38 48 58
continuous curve 273 295 301
Continuous time 5
Cooling 27 48
Credit card debt 77
de Moivre's formula 240
Death rate 23
demand 24 91—93 193 194 269
Demand, Linear Price-Demand Model 194
Demand, Linear Price-Demand-Supply Model 193
Demand, Nonlinear Price-Demand Model 270
Dense orbit 178 296
Dense set 178 302—304
Density dependence 88 89 97 101 267 268
Derivative see also "Differential equation(s)"
Derivative and bifurcation, fixed point 166
Derivative and bifurcation, m-cycle 171
Derivative and linearization 124
Derivative and Lyapunov exponent 181 182
Derivative and Newton Root-Finding Method 129 133
Derivative and oscillation 119
Derivative and stability, differential equation 137
Derivative and stability, differential equation, 2-cycle 146 160—162
Derivative and stability, differential equation, fixed point 119 157—162
Derivative and stability, differential equation, m-cycle 151
Determinant 215
Determinant and eigenvalues 226
Determinant and inverse matrix 215
Determinant and nontrivial solutions 215 216
Deterministic process 2 4 177 307
Differential equation(s) 3 5 6 133 134
Differential equation(s), autonomous 136
Differential equation(s), autonomous, fixed point 137
Differential equation(s), autonomous, system of 275 301 302
Differential equation(s), Euler method 133—138 275 302
Dimension (of a fractal) 309—311
Direct numerical iteration 8
Discrete dynamical system 6
Discrete time 5
Disease see "Contagious disease"
Drum 10
Dynamical system 2
Dynamical systems approach 75
Education 65 67
Eigenvalue Formula 226
Eigenvalue(s) 220—222 225 226
Eigenvalue(s), complex conjugate 244 245
Eigenvalue(s), complex conjugate, homogeneous solution 246 247
Eigenvalue(s), complex conjugate, Hopf bifurcation 291
Eigenvalue(s), complex conjugate, rotation 247—249 256 279 292 293
Eigenvalue(s), complex conjugate, stability 250 256 279 283 288 289
Eigenvalue(s), one repeated real 229 230
Eigenvalue(s), one repeated real, homogeneous solution 231—233
| Eigenvalue(s), one repeated real, stability 233 256 279 283
Eigenvalue(s), two real distinct 223
Eigenvalue(s), two real distinct, bifurcation 290 291
Eigenvalue(s), two real distinct, homogeneous solution 223—225
Eigenvalue(s), two real distinct, stability 223 256 279 283 288 289
Eigenvector(s) 220—225
Empirical model 83 84
Equilibrium point see "Fixed point"
Error 137 138
Euler method 133—138
Euler Method for a system 275 302
Euler's formula 240
Exact solution 12 see
Excel, Microsoft 33 315—319
Exponential function 44
Exponential function, growth/decay of 44 181 199 200
Falling object 2—5 19 133 140
Fibonacci equation 196
Filtering 27 38 48 58
Fixed point, differential equation 137
Fixed point, linear equation 71—74
Fixed point, linear system 204—206
Fixed point, linear system, homogeneous 233 234 250
Fixed point, linear system, non-homogeneous 255 256
Fixed point, nonlinear equation 103—106 119 124
Fixed point, nonlinear system 270 271 277—281 291
Fixed point, parameterized see "Parameterized family/system"
Flu 76
Formula for exact solution 12 see
Fractal 14 176 186 302—311
Fractal, Barnsley fern 309
Fractal, Cantor set 303 304 311
Fractal, dimension 309—311
Fractal, iterated-function system 307—309
Fractal, Julia set 305—307
Fractal, Mandelbrot map/system 14 293—295 307 308
Fractal, Mandelbrot set 294 305
Fractal, Sierpinski triangle 308 311
Frequency distribution 179 see
Generation 23 65 261 263 see
Geometric series 50—52
Global stability 106 184 271
Growth rate 23 24 88 89 190—193 266—268
Harvesting 24 153 163 192 193
Henon map 301
histogram see also "Frequency distribution"
Histogram, using Mathematica 322
Histogram, using Microsoft Excel 317 318
Homeowners 67
Homoclinic orbit, nonlinear equation 184 185
Homoclinic orbit, nonlinear system 288 289
Homogeneous linear equation 39
Homogeneous linear equation, autonomous 43 see
Homogeneous linear equation, non-autonomous 40
Homogeneous linear system 197 219
Homogeneous linear system, fixed point 204—206
Homogeneous linear system, rotation 247—249
Homogeneous linear system, solution, complex eigenvalues 246 247
Homogeneous linear system, solution, one repeated eigenvalue 231 233
Homogeneous linear system, solution, two real eigenvalues 223—225
Homogeneous linear system, stability, complex eigenvalues 250
Homogeneous linear system, stability, one repeated eigenvalue 234
Homogeneous linear system, stability, two real eigenvalues 223
Homogeneous system of simultaneous equations 215 216
Hopf bifurcation 291—293
Horseshoe, nonlinear equation 183
Horseshoe, nonlinear system 296—298
Host 190
Hyperbolic trajectory 203 206 224 272 280
Identity matrix 213 226—228 264
Imaginary axis 240
Imaginary number 236 237 246
Imaginary part 238 246
Immigration 24 191—193
Income mobility 261 263
Infection see "Contagious Disease"
Infection rate 90 99 167 268 269 288
Infection rate, periodic 99
Infinite series 52 53
Instability see "Stability"
Interest rate 11—13 21 22
Intermediate Value Theorem 153
Interval of existence/stability see also "Bifurcation"
Interval of existence/stability, nonlinear equation 157—162
Interval of existence/stability, nonlinear system 287—289
Invariant curve 273 295
Inverse equation 77 126 184
Inverse matrix 214 215
Inverse system 289 307
Irrationally periodic cycle 292 293
Irrationally periodic rotation 249 292 293
Iterate, iteration, iterative equation 8
Iterated-function system 307—309
Julia set 305—307
Julia set, using Mathematica 325
Julia set, using Microsoft Excel 319
l'Hopital's rule 51 234
Learning 93 95
Least-squares regression 78—83 96 196 197
Li, T.-Y. 184
linear combination 220 223 231 245 246
Linear Competition Model I/II 191 192
Linear equation 20 30
Linear equation, non-autonomous, homogeneous 39 40
Linear equation, non-autonomous, non-homogeneous 39 50
Linear growth 46
Linear Immigration/Migration/Harvesting Model 24
Linear model see also "Models"
Linear model, equation 9 21—25 27 48 76 77
Linear model, Markov process, three-state 256—264
Linear model, Markov process, two-state 62—68
Linear model, system 190—194
Linear Overlapping-Generations Model I/II 192 193
Linear Population Model 23
Linear Prey-Predator Model I/II 190 191
Linear Price Model 25
Linear Price-Demand Model 194
Linear Price-Demand-Supply Model 193
Linear regression 78—84 196 197
Linear system 189 197
Linear system of simultaneous equations 213—216
Linearization 124 276—279
Linearization, matrix see "Matrix of partial derivatives"
Loan 22 60
Loan Payment Formulas 60
Loan Payment Model 22
Local stability 106 271 276—279 see
Logarithmic scale 46
Logistic differential equation 134
Logistic equation 89 97 155 156
Logistic family 155 156
Logistic family, bifurcation 165 166
Logistic family, chaos 176—180 183 185
Logistic family, intervals of stability 158 160 161
Logistic family, period doubling cascade 169—173 176 177
Long-term behavior 17 69 see
Lorenz system 301 302
Lorenz, E. 302
Lyapunov exponent 180—182
Lyapunov exponent, using Mathematica 321 322
Lyapunov exponent, using Microsoft Excel 317
m-cycle see also "2-cycle"
m-cycle, nonlinear equation 147—152
m-cycle, nonlinear system 282—284
m-cycle, parameterized see "Parameterized family/system"
Maclaurin series 244
Mandelbrot map/system 14 293—295 307
Mandelbrot set 294 305
Mandelbrot, B. 14
Market share 67 263
|
|
|
| Реклама |
|
|
|
|
|
О проекте