The adaptive dual synchronization of chaotic (hyperchaotic) complex
systems with uncertain parameters has been investigated. The analytical
control functions are derived using a theorem to synchronize the chaotic
(hyperchaotic) solutions of these systems. The adaptive dual synchronization
between the chaotic complex Chen and Lorenz systems is introduced
as an example, and another example is used to test the validity
of the technique of this paper. Other examples of chaotic or hyperchaotic
complex systems can be similarly studied. Based on the up-to-date
laws, the parameters of the drive systems can be identified. The image encryption
technique based on the adaptive dual synchronization of chaotic
complex Chen and Lorenz systems is presented for gray and color images
in the same time. Meantime, in the receiver side, information can be recovered
successfully by adaptive technique. The presented technique is robust
with respect to different levels of white Gaussian noise. The communication
channel as well as the effect of the increase of noise are big challenge
which have not been considered. Numerical simulations are given to verify
the feasibility of our proposed synchronization and better performance of
image encryption technique in terms of histogram, robustness to noise and
visual imperceptibility.