| In recent years, scholars have paid more attention to the chaos research. Various new chaotic systems have been discovered and presented, which enrich and improve the research content of chaos, and make chaos in the fields of image encryption, video encryption, secure communication, fault diagnosis and other areas of the practical application range more wide. In this research, the main work of this paper is:1. A novel three-dimensional autonomous chaotic system is proposed in this paper.The dynamic behaviors of the proposed system are studied. The theoretical analysis and numerical simulation results imply that there exists a chaotic attractor in the system with a certain range of change on system parameters. On the basis, the topological horseshoe lemma is used to determine the existence of the chaotic attractors. And the analog circuit of the chaotic system is designed. The physical realization of the chaotic system is carried out.In addition, the design method of synchronization of the new chaotic system is analyzed. A kind of anti-synchronization scheme is designed by using the global control method. The synchronization scheme is verified from several different points,such as the theoretical analysis, numerical simulation, circuit design and circuit implementation. The chaotic system is applied in secure communication on chaos masking technology, which have good application prospects.2. Based on the new integer-order chaotic system,a novel fractional-order chaotic system is regarded as research object, and chaotic characteristics are deeply studied. At first,the results of the phase trajectory diagrams, Lyapunov exponent spectra and bifurcation diagrams of the fractional-order chaotic system are based on the predictor-corrector time domain method. The results imply there exists a chaotic attractor in the system with a certain range of change on system parameters. On this basis, the synchronization of the fractional-order chaotic system is investigated. Based on the pole assignment method and the extended nonlinear state observer theory,a projection synchronization scheme is designed. This control scheme can be used in secure communication. The results of numerical simulation demonstrate the effectiveness and feasibility of the proposed method.The modified circuit design method is used. With the help of the Multisim circuit simulation software, the fractional-order system and the synchronous analog circuits is designed. The phase trajectories of the chaotic attractor and the synchronization of the system are observed through an oscilloscope.3. The proposed new fractional-order chaotic system is applied to the chaotic encryption of digital image, and some evaluation indexes of image encryption are given.The encryption scheme of the digital image is designed by using the algorithm of XOR or spatial encryption, and the digital image is encrypted and decrypted. Histogram, the correlation of adjacent pixels and secret key sensitivity are studied. The analysis results show that the image encryption algorithm based on the new fractional-order chaotic system has the characteristics of large secret key space, uniform cipher-text distribution and high security, which show that the system is effective and feasible for digital image encryption. |
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