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Marotto F. — Introduction to Mathematical Modeling Using Discrete Dynamical Systems
Marotto F. — Introduction to Mathematical Modeling Using Discrete Dynamical Systems

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Название: Introduction to Mathematical Modeling Using Discrete Dynamical Systems

Автор: Marotto F.

Аннотация:

MATHEMATICAL MODELING USING DISCRETE DYNAMICAL SYSTEMS! This mathematics text introduces powerful mathematical modeling techniques while providing you with the tools you need to succeed. Exercises with answers, suggested computer projects with specific instructions for their completion, and the book-specific website are just a few of the tools that will help you master the material. Coverage of current research, such as dynamical systems, shows you that mathematics is a vibrant and evolving discipline.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 361

Добавлена в каталог: 25.10.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
1 2 3
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