Adaptive Generalized Function Projective Lag Synchronization and Parameter Identification of Hyperchaotic Systems

Generalized function projective lag synchronization (GFPLS) is characterized by the output of the drive system proportionally lagging behind the output of the response system and ratio of the two systems is desired function scaling matrix. In this paper, GFPLS between different hyper chaotic systems with uncertain parameters, i.e. GFPLS between Lorenz-Stenflo (LS) and Lü hyper chaotic system, is studied by applying an adaptive control method. The adaptive controllers and corresponding parameter update rules are constructed to make the states of two diverse hyper chaotic systems asymptotically synchronize up to the desired scaling matrix and to estimate the uncertain parameters. The numerical simulations are provided to show the effectiveness of the results.