| 1. |
Systems with Multiple Equilibria |
| 1.1 |
Global Properties |
| 1.2 |
Feedback Control Equations |
| 1.3 |
The Transfer Function |
| 1.4 |
The Yakubovich-Kalman Theorem |
| 2. |
Pendulum-Like Systems |
| 2.1 |
The Two Canonical Forms |
| 2.2 |
Second-order Pendulum-Like Systems |
|
a) General Properties |
|
b) The Case
rS0 |
|
c) The Case r=0. Existence
of Separatrix-Loops |
|
d) Non-Local Bifurcations in the Case
r>0
|
|
e) Several Remarks about the Case r
i
(-1/a,0) |
| 2.3 |
The Lyapunov Direct Method in the Standard Form |
| 2.4 |
Monostability and Gradient-Like Behavior of Phase-Controlled
Systems with Nonlinearities having Mean Value Zero |
| 3. |
Invariant Cones |
| 3.1 |
Extension of the Circle Criterion |
| 3.2 |
Systems with One Nonlinearity and a Bounded Forcing Term |
| 3.3 |
Systems with Vector-Valued Nonlinearities |
| 3.4 |
Bakaev Stability |
| 4. |
The Bakaev-Guzh Technique |
| 4.1 |
Basic Tools for Vector Fields on Riemannian Manifolds |
| 4.2 |
Lyapunov-Type Results for Boundedness and Convergence |
| 4.3 |
The Bakaev-Guzh Technique for Vector Fields |
| 4.4 |
Second Order Systems of the Josephson-Type |
| 5. |
The Method of Non-Local Reduction |
| 5.1 |
A Lyapunov-Type Theorem |
| 5.2 |
The Idea of Non-Local Reduction for Autonomous Systems of Indirect
Control |
| 5.3 |
Gradient-Like Behavior of Pendulum-Like Systems |
| 5.4 |
Gradient-Like Behavior of Equations studied in the Theory of
Phase-locked loops |
| 5.5 |
Non-Local Reduction of Higher dimensional Systems to Autonomous Systems
in the Plane |
| 5.6 |
Non-Local Reduction in Non-Autonomous Pendulum-Like Systems |
| 5.7 |
A Constructive Approach for Determining Lagrange Stability Criteria
in the Non-Autonomous Case |
| 6. |
Circular Solutions and Cycles |
| 6.1 |
Pendulum-Like Systems with a Single Sign-Constant Nonlinearity |
| 6.2 |
Frequency-domain Conditions for Existence of Circular Solutions and
Cycles of the Second Kind |
| 6.3 |
Circular Solutions and Cycles of the Second Kind in Concrete
Systems of Phase Synchronization |
| 6.4 |
Cycles of the First Kind |
| 7. |
Synchronous Machines Equations |
| 7.1 |
Special Properties of Synchronous Machines Equations |
| 7.2 |
Gradient-Like Behavior of Machine Equations with a Zero Load |
| 7.3 |
Application of Non-Local Reduction Method to some Classes of
Synchronous Machines |
| 7.4 |
Synchronous Machines Equations with a Forcing Term |
| 7.5 |
The Equation of a Synchronous Machine with a Speed Governor |
| 7.6 |
The Dynamics of Two Coupled Synchronous Machines |
| 8. |
Integro-Differential Equations |
| 8.1 |
General Setting |
| 8.2 |
A priori Integral Estimates |
| 8.3 |
Bakaev-Guzh Technique |
| 8.4 |
Non-Local Reduction Principle |
| 8.5 |
Phase Synchronization Systems |
| 9. |
Cycle Slipping in Phase-Controlled Systems |
| 9.1 |
Frequency-Domain Conditions for Cycle Slipping in ODE´s |
| 9.2 |
Distributed Parameter Systems |
| 10. |
Discrete Systems |
| 10.1 |
Introduction |
| 10.2 |
Boundedness by Positively Invariant Cones |
| 10.3 |
Bakaev-Guzh Technique for Discrete Systems |
| 10.4 |
The Method of Non-Local Reduction |
