Shape Synchronization Of Chaotic System And Its Application Study In Secure Communication System

With the increasing popularity of network information technology, secure communication has become one of the key technologies in information processing and automatic control. Search for new secure communication algorithms and strategies is increasingly becoming the focus of computer science and technology, control science and engineering, applied mathematics and other disciplines. It is worth noting that the nature of the use of chaotic signals to study secure communication algorithm and strategy is one of the important research directions. Chaotic signal has the properties of ergodic, non periodic, continuous broadband frequency spectrum, noise like and so on. The results show that these features are helpful to communication encryption and image encryption. With the further research on the chaotic system, the research on the control of the chaotic system has attracted the attention of people. The most important type of synchronization is complete synchronization, generalized synchronization, phase synchronization, lag synchronization. At present, the research on the new algorithm of chaos synchronization control and the application of the new method of secure communication is still in the stage of exploration and development.The main content of this paper contains the analysis of the shape synchronization of continuous chaotic dynamical system and its application study on secret communication. Aimed to two and three dimensional continuous chaotic system,by utilizing the basic theory of plane curves in classical differential geometry, desigining shape synchronization cotroller, two systems achieved drive-response shape synchronization.The chaotic masking has been developed for shape synchronized chaotic communication system. The innovation of this paper is mainly reflected in the following aspects:1. Control and research on the drive-response shape synchronization for two dimensional continuous chaotic systems. At first, the definition of the shape synchronization of a two dimensional continuous chaotic system is given. Then based on the signed curvatures and arc length of chaotic attractor, we have designed the shape synchronization controller. The simulation shows that the two systems have the same chaotic attractors shape as in the phase plane, but are located in different positions.The two systems that achieve shape synchronization are just only the same shape, and the corresponding state variable is not equal.2. Research on the shape synchronization secures communication for two dimensional continuous chaotic systems. A scheme of secure communication system is proposed based on drive-response shape synchronization for two dimensional continuous chaotic systems. In most secure communication systems, the transmited signal not only as the carrier of the original useful signal but also as a driving signal is transmitted via the public channel.In our proposed scheme, the driving signal and the useful signal are used to masked the transmission in different channels. And the driving signal is the chaotic signal after the complex processing of the two output chaotic signal of the drive system, which represents the shape of the chaotic attractor of the drive system. The original useful signal is transmitted to the receivied side of the chaotic output of the drive system via an adder. When the received side receives the initial information of the drive system encrypted by the encryption function, the chaotic attractor of reponse system is completely coincident with the chaotic attractor of drive system by translation and rotation. Eventually, the original useful signal is recovered. Simulation results show that the original useful signal can be recovered from the initial time.The secure communication method based on shape synchronization has obvious advantages, which enhance the security and flexibility of secures communication based on shape synchronization.And multi channel secure communication system has strong robustness to noise.3. Control and research on the shape synchronization for three dimensional continuous chaotic systems. At first, the definition of the shape synchronization of a three dimensional continuous chaotic system is given. Three projection systems of the drive system are obtained by reducing the dimension of 3D continuous chaos.Based on the signed curvatures and arc length of plane curves; we have designed the shape synchronization controller for three projection system, which achieve shape synchronization between the three projection systems and the corresponding response systems The simulation shows the effection of shape synchronization controllers.4. Research on the shape synchronization secures communication based on three dimensional continuous chaotic systems. For the three dimensional continuous chaotic system, two schemes of multi channel secure communication system are presented. In first scheme, the original useful one dimensional signal is masked by the output chaotics singals of the drive system then transmitted through the public channel. The driving signals through the signal synthesizer to extract the characteristic variables of the chaotic attractor of the two driving projection system are transmitted from the transmit side to the received side.On the effeciton of shape synchronization controllers, the two systems are achieved shape synchronization.When the received side receives the initial information of the drive system encrypted by the encryption function, the chaotic attractor of reponse systems is completely coincident with the chaotic attractor of drive projection systems by translation and rotation. Eventually, the original useful signal is recovered. In second scheme, three dimensional signals are decomposed into three one-dimensional signals, which are masked by the output chaotics singals of the drive system then transmitted through the public channel. The signal synthesizer extracts the characteristic variables of the chaotic attractor of the three driven projection system as the driving signal to the received side. On the effeciton of shape synchronization controllers, the two systems are achieved shape synchronization.When the received side receives the initial information of the drive system encrypted by the encryption function, the reconstruction of the space curve is restructured by the reconstruction device, which complete coincidence of the chaotic attractor of drive system. Eventually, the original useful signal is recovered.This dissertation was supported by the National Science Foundation of China (61273219), the National Science Foundation of Guangdong Province of China (S2013010015768) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20134420110003).