The second part of the course introduces the notion of chaos and discusses various cases of synchronized chaotic oscillation, such as identical synchronization, generalized synchronization and phase synchronization. The examples used here are based on electronic circuits and biological systems with an emphasis on applications, in particular on the use of chaos in secure communications. The course will emphasize the use of analytical and semi-analytical methods in studying synchronization. Introduction to Nonlinear Dynamics. Synchronization in Periodic Oscillators.
Synchronization phenomena in nature and technology.
Introduction to bifurcations on a phase plane. Floquet multipliers and characteristic exponents. Self-sustained oscillations in autonomous dissipative systems. Systems with cylindrical phase space. Dynamics of phase lock loops.