Contributors |
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xiii | |
Preface |
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xvii | |
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Part I New Chaotic Systems: Design and Analysis |
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1 Experimental Observations and Circuit Realization of a Jerk Chaotic System With Piecewise Nonlinear Function |
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3 | (20) |
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3 | (1) |
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2 Mathematical Model and Basic Properties |
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4 | (1) |
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5 | (8) |
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3.1 Equilibrium and Stability |
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5 | (5) |
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10 | (1) |
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3.3 Lyapunov Exponents Analysis |
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11 | (1) |
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12 | (1) |
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13 | (4) |
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17 | (1) |
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18 | (2) |
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20 | (3) |
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2 Analytical, Numerical and Experimental Analysis of an RC Autonomous Circuit With Diodes in Antiparallel |
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23 | (18) |
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23 | (2) |
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2 Analysis of Autonomous RC Circuit With Diodes in Antiparallel |
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25 | (11) |
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2.1 Symmetry, Invariance, Dissipative Character, and Linear Stability of the Equilibrium Points |
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26 | (3) |
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2.2 Dynamical Behaviors of the Circuit |
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29 | (6) |
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2.3 Observation of Chaotic Attractors From the Oscilloscope |
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35 | (1) |
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36 | (1) |
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37 | (1) |
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37 | (4) |
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3 Chaos in a System With Parabolic Equilibrium |
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41 | (22) |
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Sundarapandian Vaidyanathan |
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41 | (2) |
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2 Model of a System With Infinite Equilibria |
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43 | (1) |
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3 Dynamical Properties of the System With Parabolic Equilibrium |
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44 | (1) |
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3.1 Equilibrium Points and Stability |
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44 | (1) |
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45 | (1) |
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4 Circuitry Implementation of the System With Parabolic Equilibrium |
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45 | (3) |
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5 Adaptive Control of the System With Parabolic Equilibrium |
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48 | (4) |
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6 Adaptive Synchronization of Two Systems With Parabolic Equilibrium |
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52 | (3) |
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55 | (3) |
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58 | (1) |
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58 | (1) |
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58 | (5) |
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4 A New Four-Dimensional Chaotic System With No Equilibrium Point |
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63 | (14) |
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63 | (1) |
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2 New No Equilibrium Chaotic System |
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64 | (1) |
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3 Fractional Order Hyperjerk System (FOHJS) |
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65 | (5) |
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68 | (2) |
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70 | (2) |
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72 | (1) |
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72 | (5) |
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5 A New Five Dimensional Multistable Chaotic System With Hidden Attractors |
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77 | (12) |
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77 | (1) |
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2 New System and Its Dynamical Properties |
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78 | (1) |
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3 Digital Implementation for the System Using Field Programmable Gate Arrays |
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78 | (4) |
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82 | (2) |
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84 | (1) |
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84 | (1) |
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84 | (5) |
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6 Extreme Multistability in a Hyperjerk Memristive System With Hidden Attractors |
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89 | (16) |
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89 | (2) |
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2 The Hyperjerk Memristive System |
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91 | (5) |
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3 System's Extreme Multistability |
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96 | (5) |
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101 | (1) |
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101 | (2) |
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103 | (2) |
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7 Parameter Estimation of Chaotic Systems Using Density Estimation of Strange Attractors in the State Space |
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105 | (22) |
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105 | (1) |
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2 A New Chaotic System and Its Bifurcation Analysis |
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106 | (1) |
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3 Density Estimation of the Attractor in the State Space Using GMM |
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107 | (5) |
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109 | (1) |
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110 | (1) |
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110 | (1) |
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3.4 Likelihood Score Evaluation |
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110 | (1) |
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3.5 Determining the Appropriate Number of Gaussian Components |
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111 | (1) |
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4 Parameter Estimation of the Chaotic System Using GMM-Based Cost Functions |
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112 | (1) |
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112 | (1) |
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112 | (1) |
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113 | (9) |
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5.1 The GMM of the Chaotic System |
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113 | (2) |
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5.2 1D Parameter Estimation of the Chaotic System |
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115 | (1) |
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5.3 The Effect of the Length of the Evaluation Data |
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116 | (4) |
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5.4 2D Parameter Estimation of the Chaotic System |
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120 | (2) |
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122 | (1) |
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123 | (1) |
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123 | (4) |
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Part II Real World Applications |
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8 Virtualization of Chua's Circuit State Space |
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127 | (38) |
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127 | (1) |
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128 | (1) |
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129 | (1) |
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4 Virtual Reality and Other Visualization Forms |
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130 | (5) |
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4.1 3D Virtualization Sequence and Its Implementation |
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130 | (1) |
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4.2 Input Data Preparation and Acquisition |
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131 | (1) |
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4.3 Modeling, Editing and Verification |
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131 | (1) |
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4.4 Visualization and Working With Virtual World |
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132 | (1) |
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133 | (1) |
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4.6 3D Printing and Real Objects Creation |
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134 | (1) |
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5 Visualization and Immersive Environments |
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135 | (2) |
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5.1 Mixed Reality System Implementation |
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136 | (1) |
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5.2 CAVE System Implementation |
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137 | (1) |
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6 Visualization of Objects in State Space |
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137 | (14) |
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6.1 Visualization of a Chaotic Attractor by Software Means |
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138 | (7) |
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145 | (6) |
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6.3 Visualization in Virtual Cave Environment |
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151 | (1) |
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7 Possibilities of Calculation of C-SBS |
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151 | (8) |
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7.1 Calculation of C-SBS by a PC With Single or Multicore Processor |
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154 | (5) |
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7.2 GRID Technology or High-Performance Computer Clusters |
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159 | (1) |
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7.3 GPGPU Technology Usage |
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159 | (1) |
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159 | (1) |
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160 | (5) |
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9 Some New Chaotic Maps With Application in Stochastic |
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165 | (22) |
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165 | (1) |
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2 One-dimensional White Gaussian Noise Generator |
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166 | (9) |
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3 Attention Deficit Disorder Model |
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175 | (6) |
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4 Discussion and Conclusion |
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181 | (1) |
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182 | (5) |
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10 Chaotic Solutions in a Forced Two-Dimensional Hindmarsh-Rose Neuron |
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187 | (24) |
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187 | (3) |
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190 | (1) |
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3 Numerical Results of the Bifurcation Analysis |
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191 | (3) |
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4 Numerical Results of Wave Propagation in the Designed Network |
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194 | (12) |
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206 | (1) |
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207 | (4) |
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11 PD Bifurcation and Chaos Behavior in a Predator-Prey Model With Allee Effect and Seasonal Perturbation |
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211 | (22) |
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211 | (1) |
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212 | (1) |
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213 | (1) |
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4 Dynamical Analysis of System for Both Types of Allee Effect |
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213 | (4) |
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217 | (13) |
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5.1 Predator-Prey System With Strong Allee Effect |
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217 | (4) |
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5.2 Predator-Prey System With Weak Allee Effect Case Study |
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221 | (6) |
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5.3 Seasonally Perturbed System |
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227 | (3) |
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230 | (1) |
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231 | (2) |
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12 Chaotic Path Planning for a Two-Link Flexible Robot Manipulator Using a Composite Control Technique |
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233 | (28) |
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233 | (3) |
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2 Modeling of the Two-Link Flexible Manipulator |
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236 | (3) |
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3 Singular Perturbation Modeling of a TLFM |
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239 | (2) |
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3.1 Dynamic Model of the Slow Subsystem |
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240 | (1) |
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3.2 Dynamic Model of the Fast Subsystem |
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240 | (1) |
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4 Design of a Composite Control |
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241 | (3) |
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4.1 Dynamic Surface Control of the Slow Subsystem |
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241 | (1) |
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4.2 Backstepping Control for the Fast Subsystem |
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242 | (2) |
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5 Chaotic Signal as the Desired Trajectory |
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244 | (1) |
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6 Results and Discussion for the Composite Control |
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244 | (8) |
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6.1 Simulation Results With the Nominal Payload (0.145 kg) |
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245 | (3) |
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6.2 Chaotic Trajectory Tracking With a 0.3 kg Payload |
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248 | (4) |
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252 | (1) |
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252 | (9) |
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Part III New Trends in Chaos Synchronization |
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13 Robust Synchronization of Master Slave Chaotic Systems: A Continuous Sliding-Mode Control Approach With Experimental Study |
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261 | (16) |
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261 | (2) |
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263 | (1) |
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263 | (1) |
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4 Output-Feedback-Based Continuous Singular Terminal Sliding-Mode (CSTSM) Controller Design |
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264 | (3) |
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4.1 Finite-Time Sliding-Mode Observer |
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266 | (1) |
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5 Numerical Simulation Results |
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267 | (3) |
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270 | (2) |
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272 | (1) |
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273 | (4) |
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14 A Four-Dimensional Chaotic System With One or Without Equilibrium Points: Dynamical Analysis and Its Application to Text Encryption |
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277 | (24) |
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277 | (2) |
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2 Model of Proposed Autonomous System With One or Without Equilibrium Points |
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279 | (1) |
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3 Dynamical Analysis of Proposed Autonomous System With One or Without Equilibrium Points |
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280 | (7) |
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3.1 Self-Excited Attractor in Proposed Autonomous System With Only One Equilibrium Point |
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280 | (1) |
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3.2 Hidden Attractor in Proposed Autonomous System Without Equilibrium Point |
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281 | (6) |
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4 Electronic Circuit Implementation of Proposed Autonomous System With One or Without Equilibrium Points |
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287 | (4) |
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5 Adaptive Finite-Time Synchronization of Proposed Autonomous System With Hidden Attractor |
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291 | (5) |
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292 | (1) |
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293 | (2) |
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5.3 Numerical Verifications |
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295 | (1) |
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6 A Text Encryption Application Using Hidden Chaotic Attractor of Proposed Autonomous System With One or Without Equilibrium Points |
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296 | (2) |
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6.1 Proposed Affine Cipher |
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296 | (1) |
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296 | (1) |
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6.3 Numerical Verifications |
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297 | (1) |
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298 | (1) |
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299 | (2) |
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15 FPGA Implementation of Chaotic Oscillators, Their Synchronization, and Application to Secure Communications |
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301 | (28) |
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Jose de Jesus Rangel-Magdaleno |
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301 | (2) |
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2 Simulation of Chaotic Oscillators Based on PVVL Functions |
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303 | (3) |
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2.1 Numerical Methods to Simulate Chaotic Oscillators |
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305 | (1) |
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2.2 Simulation of the PWL-Function-Based Chaotic Oscillators |
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306 | (1) |
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3 Cosimulation Between Active-HDL and Simulink |
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306 | (5) |
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4 Experimental Observation of Chaotic Attractors and Synchronization of Two Chaotic Oscillators |
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311 | (8) |
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4.1 Synchronization in a Master-Slave Topology |
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316 | (3) |
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4.2 Synchronization in a Master-Slave Topology for the Three Chaotic Oscillators |
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319 | (4) |
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5 Application to Image Transmission |
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323 | (3) |
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326 | (1) |
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326 | (1) |
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326 | (3) |
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16 On Nonidentical Discrete-Time Hyperchaotic Systems Synchronization: Towards Secure Medical Image Transmission |
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329 | (22) |
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329 | (2) |
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2 Proposed Method for Coupled Nonidentical Chaotic Systems Synchronization Study |
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331 | (6) |
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2.1 Proposed Synchronization Method: Basic Idea |
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331 | (2) |
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2.2 Case of the Synchronization of Wang System Coupled to Henon Hitzl Zele System |
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333 | (3) |
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2.3 Case of the Synchronization of Generalized Henon 3D System Coupled to Stefanski System |
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336 | (1) |
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3 Proposed Cryptosystem to Secure Medical Images Based on Coupled Hyperchaotic Henon 3D and Stefanski Systems Synchronization |
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337 | (8) |
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3.1 Cryptosystem Design: Problem Statement |
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337 | (2) |
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3.2 Encryption and Decryption Process and Results |
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339 | (2) |
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3.3 Measurement of Encryption and Decryption Quality |
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341 | (1) |
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341 | (4) |
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345 | (1) |
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345 | (1) |
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346 | (1) |
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346 | (3) |
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349 | (2) |
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17 Fractional-Order Hybrid Synchronization for Multiple Hyperchaotic Systems |
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351 | (16) |
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351 | (1) |
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2 Preliminaries and Problem Position |
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352 | (2) |
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352 | (1) |
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353 | (1) |
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354 | (2) |
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4 Hybrid Synchronization Between Identical FO Hyperchaotic Systems |
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356 | (4) |
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4.1 FO Hyperchaotic Systems |
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356 | (1) |
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357 | (1) |
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358 | (2) |
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5 Hybrid Synchronization Between Nonidentical FO Hyperchaotic Systems |
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360 | (3) |
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5.1 Different FO Hyperchaotic Systems |
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360 | (1) |
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361 | (2) |
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363 | (1) |
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363 | (2) |
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365 | (1) |
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366 | (1) |
Index |
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