Spatiotemporal combination synchronization of different nonlinear objects

This paper proposes a novel secure communication scheme based on the Karhunen–Loéve decomposition and the synchronization of a master and a slave hyperchaotic Lü systems. First, the Karhunen–Loéve decomposition is used as a data reduction tool to generate data coefficients and eigenfunctions that capture the essence of grayscale and color images in an optimal manner. It is noted that the original images can be reproduced using only the most energetic eigenfunctions; this results in computational savings. The data coefficients are encrypted and transmitted using a master hyperchaotic Lü system. These coefficients are then recovered at the receiver end using a sliding mode controller to synchronize two hyperchaotic Lü systems. Simulation results are presented to illustrate the ability of the proposed control law to synchronize the master and slave hyperchaotic Lü systems. Moreover, the original images are recovered by using the decrypted data coefficients in conjunction with the eigenfunctions of the image. Computer simulation results are provided to show the excellent performance of the proposed scheme.