Page 694 - Mathematical Techniques of Fractional Order Systems

666 Index

Controllability results (Continued) Distributed order RC electrical circuit, exact
existence of mild solution, 212 222 response of, 123 124
existence of optimal control, 222 225 Disturbance rejection
preliminaries, 209 225 when disturbance is injected at controller
Controlled Picard’s method (CPM), 43 45, output, 270 272
70 when disturbance is injected at plant output,
Controller design 273 274
for stabilization, 570 574, 576 579 Dounford Pettis theorem, 201
for synchronization, 574 576 D-stability, 76, 80 81
Convolution power of function, 107 Dual combination synchronization, 347
Correlation dimension, 637 638 among different dimensional chaotic
Coupled fractional AL, 161, 167 systems, 361f, 367f
Coupled fractional order adaptive laws with order m . n, 362 367
(CFOAL), 167 168, 174, 175f, 176, with order n . m, 352 361
179f, 180f problem formulation, 350 352
Coupled-map lattices (CML), 428 429 Dual synchronization, 350
Covitz Nadler fixed point theorem, Duffing fractional order system, 319 321,
230 231, 246 247 454 455, 610
Cramer’s rule, 79 Duffing oscillator, 453 455
Crone approximation, 151, 174 Duffing Holmes system, 422 423, 423f
CRONE Toolbox, 151 Dynamical systems, controllability of, 229
CSF-1 (Colony-stimulating Factor 1), 12
E
D Economics and Finance (E&F) chaos
Dead-time/after-effect, 133 134 software, 515
Delay differential equations, 125 126 Electrically coupled neuron systems,
Delay-dependent condition, 138 139 synchronization of, 421 422
Delay-dependent stabilization, 148 Emden Fowler type equations, 41 43
Delay-independent condition, 138 139 Encryption applications, maps for, 377 380
Denosumab, 13 14 Endothelin, 13 14
Design of controllers, 456 464 Endothelin A receptor (ETR), 13
Determinism rate, 631, 632t Endothelin-1 (ET-1), 13
Deterministic chaos, 559 560 Equicontinuous, 198 199, 240 242
concept of, 628 633 Equilibrium points, 476, 504 505
Deterministic systems, 409 411 model and dynamics of system with infinite
Differential inclusions, theory of, 185 186, number of, 477 483
230 shape of, 478f
Differential quadrature method, 58 60 Error function, 351
Diffusion-reaction model, 51 57 Error models (EM), 159, 164
Discrete logistic equations, 389t Euler’s Gamma function, 190, 634
Discrete one-dimensional chaotic maps, 377 Exponential integral function, 105 106, 116
Discrete-time chaotic systems, 626 627
Dissipative hidden attractor
with no equilibria and quadratic F
nonlinearities, 518 Feedback control method, 626 627
with single stable equilibrium Feedback controller, 134, 252
point, 519 Feedback stabilization, 148 150
Dissipative systems, 411 based on time-delay-dependent stability
Distributed order calculus, 105, 107 condition, 149 150
Distributed order electrical circuits, 105 based on time-delay-independent stability
Distributed order operators, 103 105 condition, 148 149