Synchronization of chaotic symmetric gyros by one-way coupling conditions

A simple satellite is a symmetric gyro. Satellites are used for communications, weather forecasts, surveying and in several other scientific and military applications. In particular, for military use secure communications are very important. As chaotic signals are usually broadband and noise like, synchronized chaotic systems can be used as cipher generators for secure communication. This paper presents chaos synchronization of two identical chaotic motions of symmetric gyros. It has been demonstrated that applying four different kinds of one-way coupling conditions can synchronize two identical chaotic systems. The sign of the sub-Liapunov exponent has been used as an indicator for the occurrence of chaos synchronization. It has also been found that when chaos synchronization occurs the positive major sub-Liapunov exponent transverses the zero value and becomes negative for the last time. Chaos synchronization can also be shown by phase trajectory. In addition, synchronization time is also examined. Furthermore, it has been found that different distances of the initial conditions between the master system and slave system do not affect the occurrence of chaos synchronization.