Hi all,

I recently picked up the book titled "Equations of Phase-Locked Loops - Dynamics on Circle, Torus and Cylinder" Its Table of Contents can be found here. My math background is very little that is necessary for engineering and that was a while ago. I learned things like differential equations and their solutions, vector algebra and calculus etc but most of them forgotten as I don't have any need for them in my daily work.

I am having a hard time understanding the above book. Can you guys kindly suggest some easy going pre-reading books to understand the math used in the book. I am pasting a short-version of the table of contents below. The longer version is available in the link above. Thank You for your time.

Introduction:

- What Is Phase-Locked Loop?

- PLL and Differential or Recurrence Equations

- Averaging Method

- Organization of the Book
The First Order Continuous-Time Phase-Locked Loops:

- Equations of the System

- The Averaged Equation

- Solutions of the Basic Frequency

- Differential Equation on the Torus

- Fractional Synchronization

- The System with Rectangular Waveform Signals

- The Mapping (f
(p)=p+2πμ+asin(p)The Second Order Continuous-Time Phase-Locked Loops:

- The System with a Low-Pass Filter

- Phase-Plane Portrait of the Averaged System

- Perturbation of the Phase Difference φ
(wt)

- Stable Integral Manifold

- The PLL System Reducible to the First Order One

- Homoclinic Structures

- Boundaries of Attractive Domains

- The Smale Horseshoe, Transient Chaos

- Higher Order Systems Reducible to the Second Order Ones
One-Dimensional Discrete-Time Phase-Locked Loop:

- Recurrence Equations of the System

- Periodic Output Signals

- Rotation Interval and Frequency Locking Regions

- Stable Orbits, Hold-In Regions

- The Number of Stable Orbits

- Bifurcations of Periodic Orbits

- Bifurcation of the Rotation Interval
Two-Dimensional Discrete-Time Phase-Locked Loop:

- Description of the DPLL System by a Two-Dimensional Map

- Stable Periodic Orbits

- Reduction to a One-Dimensional System

- Strange Attractors and Chaotic Steady-States