Design Of A Class Of Chaotic Systems And Its Synchronous Control Application

Nonlinearity is the essential state of nature,and chaos theory is one of the branches of nonlinearity,which shows the unity of certainty,randomness and unpredictability.Studying chaos theory helps to understand the nature of nonlinear science,while chaos control can be applied in different research fields.Coexistence attractors exist in infinite equilibrium chaotic systems,non-equilibrium chaotic systems and stable equilibrium chaotic systems.The coexistence of multiple attractors leads to the existence of multiple stability in chaotic systems,which is of great significance to the development of chaos theory and has attracted more attention.This thesis starts with a class of infinite equilibrium chaotic systems,analyzes its nonlinear dynamics,discusses its synchronization control mechanism,and studies the application of adaptive synchronization control in color image encryption.The main research contents and results of this thesis are as follows:(1)On the basis of the literature,we construct a new infinite equilibrium point chaotic system,give the equilibrium point,stability analysis,Poincarè section analysis,Lyapunov index and bifurcation graph analysis,and study the local change bifurcation graph and the motion state of the system.Moreover,studying the multi-stability and complexity of the new system proves that the system is chaotic from multiple perspectives.Then,the circuit schematic diagram of the new system is designed to verify the circuit simulation results and numerical simulation results,and the feasibility of the system circuit realization is discussed.(2)The synchronization control of the new system is studied,and the Lyapunov stability theory is discussed to design the synchronization controller.Firstly,the active synchronization control is designed,and then the adaptive synchronization controller and parameter control strategy are designed,so that the parameters can be estimated accurately,and the system can achieve synchronization in a limited time.Secondly,the influence of control gain of synchronization system on synchronization time is studied.Experimental verification is given for the above two synchronization control methods.The results show that the control method is effective and feasible,and the advantages and disadvantages of the two methods are analyzed from the point of design and simulation.(3)An adaptive synchronization control system is proposed for color image encryption.The chaotic sequence generated by the synchronous system is processed to conform to the characteristics of the key stream,and the sequence generated by the drive system is used for encryption operation and the sequence generated by the response system is used for decryption operation.Image encryption in the scrambling stage using ascending method,in the diffusion stage using Deoxyribonucleic acid(DNA)encoding do XOR operation,get the final encrypted image.This encryption method has the characteristics of large key space strong key sensitivity and the entropy of encrypted image information is closer to the theoretical value.In this thesis,we propose a class of chaotic systems with infinite equilibrium point,analyze its nonlinear dynamic characteristics and complexity,design circuit simulation.And realize the driver-response system synchronization and image encryption application design.The results show that the proposed system has complex dynamic behavior and its co-existing attractors can be observed.The designed synchronization control system has good synchronization effect.The application of synchronous system in image encryption has a good encryption effect,which verifies the complexity and applicability of the new system.