Chaos, synchronization and structures in dynamics of systems with cylindrical phase space

Preface......Page 6
 References......Page 8
Contents......Page 9
About the Authors......Page 11
 1.1 Dynamics of Autonomous Rotator and Related Physical Systems......Page 13
 1.2 Synchronization and Chaotic Rotations of Non-autonomous Rotator......Page 21
 References......Page 35
 2.1 Dynamics of Rotator with Aperiodic Load......Page 37
 2.2 Synchronization and Dynamical Chaos in a System of Non-autonomous Rotator with Aperiodic Load......Page 46
 References......Page 60
 3.1 Dynamics of Rotator with Oscillatory Load......Page 61
 3.2 Chaotic Dynamics of a Simple Vibrational Mechanism......Page 68
 3.3 Dynamics of Coupled Rotators......Page 78
 References......Page 87
 4.1 Nonlinear Resonance of Bending Vibrations of a Flexible Rotor in a System with an Energy Source of Limited Power......Page 88
 4.2 Damping Lateral Vibrations in Rotary Machinery Using Motor Speed Modulation......Page 98
 4.3 Chaotic Torsional Vibrations of the Shaft in a System with Limited Power Source......Page 105
 References......Page 118
 5.1 Synchronization in Lattices of Dynamical Systems. General Information......Page 120
 5.2 Synchronization of Rotations in a Chain and in a Ring of Diffusive-Coupled Autonomous and Non-autonomous Rotators......Page 128
 5.3 Regular and Chaotic Synchronization in a Homogeneous Chain of Dynamical Systems of “Rotator-Oscillator” Type......Page 135
 References......Page 140
6 Physics, Existence, Fusion, and Stability of Cluster Structures......Page 142
 6.1 Physics of Cluster Structures......Page 143
 6.2 Fusion and General Properties of Circuits of Cluster Structures......Page 154
 6.3 C-Oscillators of a Chain and the Fullness of Types of Their Cluster Structures......Page 161
 6.4 C-Oscillators of a Ring and Fusion of Cluster Structures......Page 172
 6.5 Stability of Cluster Structures......Page 183
 References......Page 192
A.1 Systems of Coupled Rotators Without Additional Loads......Page 194
A.2 Systems of Coupled Rotators with Aperiodic Loads......Page 197
A.3 Systems of Coupled Rotators with Oscillatory Loads......Page 200
Appendix B Calculation of Eigenvalues of Matrices......Page 205