Study On Synchronization Of A Broadband Hyperchaotic System

Chaos is a very complex and not completely random form of motion,widely found in nonlinear systems.The initial value sensitivity and randomness of chaos make it have good application value in many fields.In recent years,the development of chaotic synchronization and control has been extremely rapid,which has aroused widespread concern in the academic community.Because hyperchaotic systems have two or more positive Lyapunov exponents,their dynamic behavior is more complex,widely used in human brain science,geology,acoustics,optics,security communication,etc,thus studying the synchronization of hyperchaotic systems has far-reaching implications.Compared with narrow-band signals,wide-band signals can carry more information,so it is more practical to study broadband in the field of signal processing such as sonar,speech recognition,and radar.In this paper,a broadband hyperchaotic system was constructed based on Chen system,and the dynamic characteristics of the system were analyzed.The maximum Lyapunov exponent of the system indicates that the phase space trajectory changes more sharply due to faster exponential growth in the same time interval;the system is always in hyperchaotic state when the system parameters change within a wide range;the bandwidth of the system is wider and it has a good application prospect in the field of secure communication.The self-synchronization problem of broadband hyperchaotic systems was studied by using nonlinear feedback synchronization method,active control synchronization method,state observer synchronization method and parameter uncertain adaptive synchronization method.Four methods were analyzed and demonstrated by theoretical derivation,numerical calculation and circuit simulation.The experimental results fully proved the effectiveness of these four methods.Finally,different structure synchronization of the broadband hyperchaotic system and the hyperchaotic Chen system was studied.The backstepping method,active control method and parameter uncertain adaptive synchronization method were used to realize different structure synchronization of the two systems.Theoretical analysis,numerical simulation and circuit simulation verified the feasibility of these three methods.