Adaptive generalized function projective synchronization of a class of new chaotic systems

Adaptive generalized function projective synchronization (GFPS) of two uncertain chaotic systems, which is a further extension of many existing projection synchronization schemes, is investigated. First, a class of new four-dimensional autonomous chaotic systems are presented, and the dynamical features are illustrated in a wide ranges of chaotic or hyperchaotic parameters by showing Lyapunov exponent spectrum, Lyapunov dimension and phase portrait. Second, based on Lyapunov stability theory, the sufficient condition to GFPS between every two of the given systems with unknown parameters is given, together with a proposed adaptive control strategy with parameter update laws. Finally, numerical simulations are demonstrated to verify the effectiveness of the presented control method.