Page 698 - Mathematical Techniques of Fractional Order Systems

670 Index

Genetic algorithm (GA) (Continued) survey of some systems with hidden
optimization of controller gains by, attractors, 507 516
265 269 Hilbert space, 187 191, 202, 208 209, 212,
description of GA, 265 266 225 226, 231, 247
tuning of controller for trajectory Hilbert-Schmidt operators, 202
tracking task, 266 269 Hille Yosida type operator, 186
Grammian matrix, 233 Holland, John, 265 266
controllability, 246 247 Homotopy analysis method (HAM), 37,
Grasshopper Optimization algorithm, 39 40, 58 60
539 540 Homotopy perturbation method (HPM),
Grey Wolf Optimization Algorithm overview 41 43, 51 53
(GWO), 534 539, 538f Homotopy series solution, 40 41
algorithm flowchart, 541f Hopfield memristive neural network, 515
technique flowchart, 538f H-valued stochastic process, 192, 203 204,
Gronwall inequality, 186 187 209, 213
Gru ¨nwald Letnikov (GL) based FPGA Hyperchaotic Henon map, 561 562
implementation of FOCS, 438 439 Hyperchaotic Lorenz system, 292
Gru ¨nwald Letnikov (GL) method, 264, 601, Hyperchaotic Ro ¨ssler’s system, 561 562
635 Hyperchaotic systems, 284 289, 294 297,
Gru ¨nwald Letnikov coefficients, 506 322
Grunwald Letnikov definition, 323, 452,
505 506, 564, 633
Gru ¨nwald Letnikov method of I
approximation, 506 Identical synchronization of fractional order
Gru ¨nwald Letnikov numerical approximation complex hyperchaotic systems,
method, 599, 616 617 299 301
IF THEN rules, 598, 602 603
Image encryption, 428 429, 429f
H Impulsive synchronization, 420
Hausdorff Besicovitch dimension, 637 Incommensurate fractional order permanent
h-curve, 45 magnet synchronous motor model,
HDL coder-based implementation of FOCS, 548 555
437 438 Incommensurate order systems, 566
Heat transfer model, 51 57 Incomplete synchronization, 420
He ´non map, 404 Information processing, 376
Hidden attractors, 503, 512t Insulin Growth Factors I and II (IGF-I, IGF-
integer and fractional order differential II), 12
equations, numerical solution of, Integer models, 16 23, 436
505 507 Integer order (IO) adaptive systems, 159
with no equilibria and quadratic Integer order error models (IOEM), 159 160,
nonlinearities, 508t 165 166
parameter variations, sensitivity to, Integer order generalized discrete maps,
516 519 377 387
conservative hidden attractor with no with scaling and shaping parameters, 387
equilibria and quadratic nonlinearities, with scaling parameters, 380 384
517 generalized logistic map with scaling
dissipative hidden attractor with no parameters, 382 383
equilibria and quadratic nonlinearities, generalized tent map with scaling
518 parameters, 383 384
dissipative hidden attractor with single with shaping parameters, 384 387
stable equilibrium point, 519 logistic map with shaping parameters,
sensitivity to fractional orders, 519 522 386