1. 
Systems with Multiple Equilibria 
1.1 
Global Properties 
1.2 
Feedback Control Equations 
1.3 
The Transfer Function 
1.4 
The YakubovichKalman Theorem 
2. 
PendulumLike Systems 
2.1 
The Two Canonical Forms 
2.2 
Secondorder PendulumLike Systems 

a) General Properties 

b) The Case
rS0 

c) The Case r=0. Existence
of SeparatrixLoops 

d) NonLocal 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 GradientLike Behavior of PhaseControlled
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 VectorValued Nonlinearities 
3.4 
Bakaev Stability 
4. 
The BakaevGuzh Technique 
4.1 
Basic Tools for Vector Fields on Riemannian Manifolds 
4.2 
LyapunovType Results for Boundedness and Convergence 
4.3 
The BakaevGuzh Technique for Vector Fields 
4.4 
Second Order Systems of the JosephsonType 
5. 
The Method of NonLocal Reduction 
5.1 
A LyapunovType Theorem 
5.2 
The Idea of NonLocal Reduction for Autonomous Systems of Indirect
Control 
5.3 
GradientLike Behavior of PendulumLike Systems 
5.4 
GradientLike Behavior of Equations studied in the Theory of
Phaselocked loops 
5.5 
NonLocal Reduction of Higher dimensional Systems to Autonomous Systems
in the Plane 
5.6 
NonLocal Reduction in NonAutonomous PendulumLike Systems 
5.7 
A Constructive Approach for Determining Lagrange Stability Criteria
in the NonAutonomous Case 
6. 
Circular Solutions and Cycles 
6.1 
PendulumLike Systems with a Single SignConstant Nonlinearity 
6.2 
Frequencydomain 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 
GradientLike Behavior of Machine Equations with a Zero Load 
7.3 
Application of NonLocal 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. 
IntegroDifferential Equations 
8.1 
General Setting 
8.2 
A priori Integral Estimates 
8.3 
BakaevGuzh Technique 
8.4 
NonLocal Reduction Principle 
8.5 
Phase Synchronization Systems 
9. 
Cycle Slipping in PhaseControlled Systems 
9.1 
FrequencyDomain 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 
BakaevGuzh Technique for Discrete Systems 
10.4 
The Method of NonLocal Reduction 