Cubic Chaotic Mapping And Its Application In Chaotic Masking Communication

Chaos theory is the most important discovery in physics in the 20th century, which is thought as the third-time important revolution of the physics of 20th century after theory of relativity and quantum mechanics. Similar to the ex- two revolutions, the chaos theory also breaks the religious rules of Newton's mechanics. There has been no one who doubts that the ability of prediction accuracy could carry out in principle, before the chaos theory was put forward. Generally, people thought that it can be carried out, if there is enough information. But the assumption was break out, when the phenomenon of chaos was found. Base upon the sensitive dependence of chaotic systems on their initial conditions, the system is almost unstable everywhere on their orbit. The system's output, with the time going by, assumes index increase because of the system's little difference of original condition and the ability of prediction will disappear completely. The phenomenon of chaos make people know the movements of external are not only in fixation or period or granted period, but also in non- period which has the more widespread meaning. Because of the phenomenon of chaos, people find there is a bridge between the system of confirmation theory and system of probability theory. And the chaos theory still can make people see many complicated phenomenon a behavior that has the purpose and the structure, but not a certain and foreign contingency behavior any more. And chaos also enriched understanding of the phenomenon which is keeping off the balance. The physical system, keeping off the balance, may be more ordinal and symmetrical or more chaotic by broken. But it is not simple out-of-order or confusion. There is not obvious period or symmetry, but it enriches the station of order. Generally, it is a phenomenon which is more universal in nature.Chaos is an outer complex behaves of nonlinear definite system, produced by the system's internal random property, a non-linear and non-random movement while it looks like random. And it is not cause by eternal factor but intrinsic factor. Then chaotic secure communication is becoming the advanced field in modern communication technique with the further research in chaos theory. Because of the property including non-period , consecutive BW spectrum and noise-like, chaotic signal is apt to secure communication.The main research work of this dissertation is clarified as followsIn chapter 1, the developing history of chaos theory and its application are reviewed. The beginning of chaos theory is in the early 20th century, when Jules Henri Poincar, the scientist of French, made the study of the problem of three objects in solar system. In 1975, Tianyan Li, scholar of China, and J. York, mathematician of American, announced the famous article 'Period Three Implies Chaos' in the 'America Mathematics', which led the 'chaos' to go into the modern science phrase. In the early 1980s, the researcher of the electronics engineering also noticed the phenomenon of chaos which appeared in the electric circuit system. In 1990, Pecora and Carroll reported that some chaotic systems can be decomposed into a drive subsystem and a response subsystem and the two subsystems can synchronize provided that all the conditional Lyapunov exponents of the response system are negative when it is driven by a signal from the drive system. Now chaotic communication has been one of the hotspots drawing attention and research of information science circle. Kinds of patterns and theories of chaotic communication have been put forward one after the other.In chapter 2, the basic knowledge of chaos theory is introduced. Because the chaotic system is really very complicated, there will be the different connotation from the different angle. Although the scientists have already studied for a century of near half, there is not a generally accepted and strictly standard mathematics definition. Definitions in common use in math consist of chaos in sense of Devaney, and chaos in sense of Li-Yorke, and chaos in sense of Melnikov. Then, in this chapter, the theory of chaotic discrete mapping is introduced, including the production of mapping, and the immobile point, and the fork. At last, in this chapter, we make deep research on the characteristics, including Lyapunov Exponent, information dimension, folk dimension, Kolmogorov entropy, of chaotic mapping.In chapter 3, we will first briefly introduce the Cubic mapping and its characteristics. At first, we introduce how to produce chaotic mapping and how to choose the parameters. Then we make deep research on the characteristics of Cubic mapping, including Lyapunov Exponent, non-period, sensitive to original condition, attractor, power spectrum, Kolmogorov entropy correlation and the balance. Given by the result of simulation, we find that a large number non-periodic, continuous broadband frequency spectrum, noise-like, but deterministic and reproducible signals can be generated by Cubic mapping.In chapter 4, we present the application of Cubic map in the chaotic signal masking to secure communication. Chaotic masking is one of the first technologies of chaotic secure communication. Simulation and data information can be transmitted by chaotic masking. Base on chaotic synchronization, chaotic masking system makes the massage sequence being recovered with chaotic sequence. Because of the noise-like, it is thought that there is just noise in channel. In the sink, the message signal is resumed. In this chapter, we present the application of Cubic map in several chaotic signal masking systems to secure communication. The simulation results for the chaotic communication systems show us, the results of secure communication are satisfied, when the Cubic mapping is applied in chaotic masking, and the results are different, when the compression coefficient (k) is different, and tow-grade modulation chaotic masking communication what is put forward can improve system's secure and anti- interference.