Page 692 - Mathematical Techniques of Fractional Order Systems

664 Index

Bone mass adaptive terminal sliding mode
density, 16 synchronization for, 292 294
evolution, 19f,20f stabilization
nonlocal simulation of, 22f,25f,31f of fractional order complex Chen chaotic
Bone metastases, 13 system, 294 295
Bone remodeling, 3, 9 23 of fractional order complex Lorenz
bone physiology, 9 14 hyperchaotic system, 296 297
creating compact biochemical bone Chaotic behavior, 319 321, 376, 415, 432,
remodeling models, 23 31 488 489, 516, 529 530, 532, 610,
integer models, 16 23 625 626
pharmacokinetics and pharmacodynamics Chaotic dynamic systems, 628 633
(PK/PD), 14 15 concept of deterministic chaos, 628 633
Bounded input and bounded output (BIBO) recurrence plot (RP), 628 630
stability, 249 250 recurrence quantification analysis (RQA),
Boussinesq problem, 41 43 631 633
Bratu’s problem, 38, 58 63 Chaotic Grasshopper Optimization Algorithm,
Brownian motions, 188, 246 539 542
Brushless DC Motor model (BLDCM), Chaotic Grasshopper Optimizer strategy
433 435 (CGOA), 540 542
Burg method, 429 430 Grasshopper Optimization algorithm
Butterfly effect, 283 284, 628 (GOA), 539 540
Chaotic Grey Wolf Optimization Algorithm,
535 539
C attacking prey (exploitation phase),
C 0 -semigroup, 186, 225 226 537 538
Caputo definition, 162 163, 489 490, 564, Chaotic Grey Wolf Optimizer strategy
634 (CGWO), 539
Caputo fractional derivative, 39, 44 45, encircling prey, 535 536
187 188, 190, 230 232, 452, 506, hunting prey, 537
600 searching for prey (exploration phase), 535
Caputo fractional operator, 186 Chaotic Lorenz system, 285, 292
Caputo fractional order derivative (FOD), phase portrait of the imaginary part of, 289f
44 45, 162 163 phase portrait of the real part of, 288f
Caputo Fabrizio’s fractional derivative, Chaotic synchronization, 418 420
226 Chaotic systems, 283 284, 348, 375 376,
Carathe ´odory multivalued map, 234 409 413, 476, 530
Cartesian coordinates, 253 fractional dynamics of, 348
Cauchy problem, 185 186, 203 204 with infinite equilibria
Center of gravity defuzzification method, antisynchronization of two identical
262 263 systems without equilibrium, 483 488
c-fms (Macrophage Colony-stimulating Factor fractional order form of system with
Receptor), 12 infinite equilibria, 488 493
Chandrasekhar model, 38 model and dynamics of system with
Chaos, 319 321, 348, 451, 476 infinite number of equilibrium points,
Chaos control, 319 321, 440 477 483
Chaos maps, 534 535 synchronization of, 283 284, 451
functions, 536t Chattering phenomenon, 606
Chaos synchronization, 283 284, 319 321, Chebyshev pseudospectral method, 41 43
349, 560 561, 597 598, 616 617 Chebyshev spectral collocation differentiation
Chaos theory, 559 560 matrix, 41 43
Chaotic and hyperchaotic systems, 286 289, Chen chaotic system, 286 287, 294
294 297 fractional order complex