Multi-scroll Chaotic System Based Circuit Design And Its Application

In nonlinear dynamical systems,chaos is a very special physical phenomenon,which has initial conditional sensitivity,pseudo-randomness,self-similarity and aperiodic continuous bandwidth spectrum.It exists widely in physics,geology,life science,social science and other fields.Chaos,quantum mechanics and the theory of relativity are the three greatest achievements of human beings in the 20 th century.In recent years,with the development of nonlinear systems,chaos science has become one of the hot spots in the information security domain.Compared with the traditional chaotic systems,the multi-scroll chaotic system has more complex topological construction,more abundant nonlinear dynamical behaviors and more flexible tremendous key space.Moreover,its orbiting can jump quickly to any of scrolls randomly in the same chaotic attractor.These features make the multi-scroll chaotic systems have a certain practical significance and application prospects.Therefore,according to chaotic theoretical basis,it is important and significant to design the complex multi-scroll chaotic system and apply it to secure communications.In this dissertation,the structural characteristics of multi-scroll chaotic systems are discussed in depth.First of all,a kind of tensile type multi-scroll chaotic attractor based on Chua's circuit is successfully designed by the same simple Heaviside functions,and the basic dynamical properties of the new chaotic system are also analyzed,either numerically or analytically.At the same time,the chaotic circuit of this system is realized by PSPICE.Using unidirectional coupled synchronization method,tensile type multi-scroll chaotic system is applied to secure communication,which verifies the availability and feasibility of the method.Then,this dissertation explores the intrinsic relationship between the chaotic system and the multi-wing attractor.And a three-dimensional multi-wing butterfly chaotic circuit is proposed by using the asymmetric mathematical model,which changes the construction method of the even symmetry function of the traditional multi-wing system.At the same time,the dynamic characteristics of the system are investigated in detail,such as chaotic attractor,time domain diagram of state variable,power spectrum,Lyapunov exponent spectrum and the complexity analysis.An electronic circuit is designed and its experimental results are presented in the digital oscilloscope,which well match the numerical simulation results.Finally,taking into account current multi-scroll chaotic circuit design is very complex,a system generally can only produce a single attractor structure.Combined with the working principle of the circuit,this dissertation further investigates an autonomous multi-scroll chaotic switch system,which first achieves the dynamic transition of different chaotic attractors for a single system.Therefore,the utilization ratio of single multi-scroll chaotic circuit is improved in the practical engineering.The basic dynamics of the system and the change of the chaotic behavior of the system under the control of the switch are analyzed by theoretical and numerical simulation.Then,the synchronization scheme of the new system is designed by using the chaos masking method,and the encryption and decryption of the information is realized,which provides a theoretical basis for the physical design and application of the multi-scroll chaotic system.