Hyperchaotic Fifth-order Autonomous Circuit Analysis And Secure Communications Applications

Chaos has been paid more attention increasely as a preceding project and science hotspot. It demonstrates the complexity caused by nonlinear phenomenon existing at large in the nature and human society, the unification of order and disorder, confirmation and randomicity. Further more it widens the sight of people in large extent and deepens our recognition of the objective world. In the field of natural and social science, its wide overcast, strong integration, far-reaching influence and wide prospect are unprecedented.The chaotic circuit and system theory has been widely regarded and applied in the field of avigation, communication and self-controlled system after thirty years of development. Because chaotic signals are typically broadband, noiselike, and difficult to predict, they are suitable to be applied to secure communications which have appealed many scholars to the research of the synchronization of chaotic and hyperchaotic systems in recent years and a great deal of instructive work has been done.A brief overview of existing works points out that most of studies have been focused on low-order systems represented as Chua's circuit in the last decades. However, high-order systems especially hyperchaotic circuits with more than two positive Lyapunov exponents can generate more complicated dynamics and are more difficult to predict using common methods such as rebuilding phase space, regress mapping and nonlinear predict. Therefore it is more significative to design and analysis the new hyperchaotic circuits in order to guarantee the safety and security in communication.On the basis of explaining the generation and development of chaos, the constraction and analysis of chaotic circuits and the methods of chaotic synchronization and secure communication, systematic research both on the theories and applications of the foregoing problems is carried out. A fifth-order autonomous hyperchaotic circuit is designed by adding a RLC parallel circuit into the L-arm in chua's circuit. Its nonlinear dynamical nature is studied deeply by the way of mathematical model, theoretical analysis and simulation. The phase portrait, poincare mapping, Lyapunov exponent spectrum and spectrum distribution character show that as the parameters are varied, the proposed circuit demonstrates periodic, chaotic and hyperchaotic oscillation. Furthermore numerical simulation shows thatthe chaotic property of the fifth-order autonomous circuit can be adjusted easily by changing R or L of the added RLC parallel circuit and it has broader parameter ranges than Chua's circuit. Therefore it has more advantages than other modified Chua's circuits when it is used in communications.Wu and Chua had proved in theory that as long as the coupling of two chaotic systems is close enough they can be synchronied well. Based on Lyapunov theory, a hyperchaotic secure communication system via the above circuit is presented whose synchronization between receiver and transmitter was realized based on the undirectionally coupled method. Also its application in secure communications is simulated. The results prove that the above hyperchaotic system can be synchronized accurately and.quickly by modifying the single feedback signal when the parameters of receiver and transmitter are suited. The results prove that this method can be widely used in secure communications.The 5-dimension dynamic hyperchaotic systems can also be synchronized under single directional feedback control of the linear combination of error variables. The possibility of system synchronization is proven by analytical deduction. Based on Lyapunov theory, the possibility of synchronization of 5D dynamic systems via single valuable uni-directional coupling is also analyzed as to obtain the necessary conditions that controller must be met for the synchronization of the two hyperchaotic systems. It has been demonstrated that when the parameters of driving system are suited to responding system, the two hyperchaotic systems can be synchronized steadily by the proposed controller. Experient results by calculating numerically and simulating with the electronic circuit show that it is possible to synchronize hyperchaos with two or more positive Lyapunov exponents by using a single controller. The results provide an important experiment evidence for the encryption communication of hyperchaos.Acording to the method of active-passive synchronization (APD) has many advantages compared to other synchronization methods, it is applied to the 5D hyperchaotic circuit synchronization and its application in secure communications is also analyzed in computer simulation. Numerical simulation shows that it is fine in security and has the good immunity to interference. And the most important character of this method lies in that we can choosedriving signals to design different chaotic or hyperchaotic systems according to different needs. Consequently it is more flexible than other methods such as the method of driving-reponding synchronization.In addition, a novel hyperchaotic secure communication system via the above circuit is presented. In the system, one sending signal is used whereas the information signal can be as large as the chaotic carrier signal. In this way, the signal-to-noise ratio and the secrecy of the system can be increased in large extent. The work process of the system is as follows: inthe sending end, the transmitted information signal s(t) is blended with the chaotic signal VCi generated by the chaotic system to creat the blended signal sd(t). Then let sd(t)through the linear transform T to prevent it from over-modulated and feedback to the main system in the form of circuit is. After the two steps modulation, the information signals(t) is blended in the chaotic signal VCi and become a noise-like chaotic signal. The output signal Vc is transmitted to the receiving end by the voltage tracker, then the useful signal can be obtained by subtracting the synchronized chaotic signal F'c from the blendedsignal s'd (/) at the receiving end.The recognition of chaos is one of the most important achievements of the non-linear science. The characteristics of chaos in itself decide its wide application prospects. Especially in recent years, the progress about chaotic synchronization and chatic control make its potential application prospects in the secure communication field with its particular charm. At present, the research of chaotic synchronization technology and its application is still developing. The problem that how to combine it with the need of every field is still being explored in order to provide new technology and methods for every applied subject.