Randomly Synchronizing Chaotic Systems

Synchronizing Chaotic Systems Summer 2006

An appropriate definition of Chaos Theory (and one of many) is “the qualitative study of unstable, aperiodic behavior in deterministic, non-linear, dynamical systems” [1]. Chaos implies that a system exhibits sensitive dependence on initial conditions. For the purposes of this research project, we are interested in two types of dynamical systems which can be chaotic. The first is a map, of the ...

Chaotic Synchronizing Systems with Zero Time

This research not only dedicated a less restrictive method of iteration-varying function for 8 a learning control law to design a controller but also synchronize two nonlinear systems with free 9 time-delay. In addition, the mathematical theory of system synchronization has proved rigorously 10 and the theory verified through an example to demonstrate the behavior of each parameter in the 11 th...

Synchronizing Autonomous Chaotic Systems Using Filters

A system for synchronizing chaotic transmitters and receivers that is less sensitive to channel effects than other known chaotic communication methods. The system employs duplicate transmitter and receiving modules and in addition to the chaotic output a synchronizing signal which occupies a reduced bandwidth. The small bandwidth affords the system a greater resistance to the affects of frequen...

Synchronizing chaotic systems using backstepping design

Backstepping design is a recursive procedure that combines the choice of a Lyapunov function with the design of a controller. In this paper it is proposed for synchronizing chaotic systems. There are several advantages in this method for synchronizing chaotic systems: (a) it presents a systematic procedure for selecting a proper controller in chaos synchronization; (b) it can be applied to a va...

Channel equalization for self-synchronizing chaotic systems