Chaotic Signals in Digital Communications

3

Overview of dynamical systems and chaos

Luiz H. A. Monteiro

Escola de Engenharia da Universidade Presbiteriana Mackenzie Escola Politécnica da Universidade de São Paulo

CONTENTS

3.1    State-variable representation and some terminology

3.2    Steady state and Lyapunov stability

3.3    Periodic and quasiperiodic solutions

3.4    Chaotic behavior

3.5    Structural stability and bifurcation

3.6    Examples: dynamics of PLLs

3.7    Concluding remarks

3.8    Acknowledgments

Bibliography

Dynamical Systems Theory (DST) is the branch of applied mathematics dedicated to qualitatively characterizing the long-term behavior of systems evolving according to difference and differential equations. DST has its roots in classical mechanics, a major area in ...