Abstract
By generalizing the classical Lorenz chaotic system, we construct the n-dimension and m-dimension dynamical systems as the drive system and response one respectively. And then we present the definitions of the dislocated function projective partial synchronization (DFPPS) and general dislocated function projective partial synchronization (GDFPPS) between the two dynamical systems. Based on Lyapunov stability theorem the controllers to realize DFPPS and GDFPPS of the two dynamical systems can be obtained in indeterminate equations. We find that no matter what dynamical behaviors the two systems have, their DFPPS and GDFPPS can be realized by controlling to partial variables (even one variable) of the response system. Three numerical examples are presented to illustrate the correctness and effectiveness of the studied results. Simultaneously, in the process of realizing GDFPPS of systems, it is important that we get a pair of more complicated time series about chaotic synchronization.
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