Observer form of the hyperbolic type generalized Lorenz system and its use for chaos synchronization

This paper shows that a large class of chaotic systems, introduced in Celikovsky and Chen [7], as the hyperbolic-type generalized Lorenz system, can be systematically used to generate synchronized chaotic oscillations. While the generalized Lorenz system unifies the famous Lorenz system and Chen's system [10], the hyperbolic-type generalized Lorenz system is in some way complementary to it. Synchronization of two such systems is made through a scalar coupling signal based on nonlinear observer design using special change of coordinates to the so-called observer canonical form of the hyperbolic-type generalized Lorenz system. The properties of the suggested synchronization that make it attractive for the the secure encrypted communication application are discussed in detail. Theoreti­ cal results are supported by the computer simulations, showing viability of the suggested approach.