Characteristcs Analysis And Control Of Several Chaotic Systems And Their Application In Image Encryption

Nonlinear phenomenoa are ubiquitous in nature.Chaos is a special motion form of nonlinear dynamic system,which reveals the complexity of nature and human society.Recently,chaotic systems have been widely concerned and applied in the fields of physics,biology,electronics,secure communication,cryptography and signal processing and detection,etc.Chaotic systems with new characteristics are constantly proposed.With the development of fractional-order calculus,it is believed that fractional-order system model has attracted more attention,which can describe the materials and processes that posses the internal memory and genetic characteristics more accurately.Therefore,it is of theoretical and practical significance to analyze the characteristics,to study the control methods,and to study the applications based on chaotic systems.In this dissertation,the dynamics feature and control of chaotic systems,and color image encryption based on chaotic systems are studied by means of theoretical analysis,numerical simulation and experiment,which provides solutions to key technologies,such as the selection and implementation of chaotic systems,and encryption algorithm based on chaotic systems in secure communications.The main research contents and results are summarized as follows:(1)Constructing high-dimensional chaotic map based on low-dimensional chaotic maps.In order to overcome the shortcomings that it is easy to predict the orbit and initial value of the low-dimensional chaotic map,a three-dimensional complex chaotic map is constructed by means of feedback coupling using several simple low-dimensional chaotic maps.Then a three-channel pseudo-random sequence generator was designed,whose randomness test was completed by using the NIST-800-22 test scheme.(2)Analysis,stabilization,and DSP-based implementation of a chaotic system with hyperbolic and nonhyperbolic equilibrium coexistence.An autonomous chaotic system with a simple algebraic structure of six terms is proposed.Basic dynamical properties of the system,including equilibrium point and their stability,phase portrait,Poincaré map,parameter bifurcation and Lyapunov exponent are studied in theory and numerical simulation.The emergence of chaos of this system is rigorously verified by the topological horseshoe theorem.Then,based on the Lyapunov stability criterion,a single variable control scheme is designed to stabilize the chaotic system to its zero-equilibrium point.The implementation scheme of attractors and control scheme are discussed in detail and realized via DSP-based technique,confirming the validity and enforceability of the theoretical analysis.(3)Exploring the dynamics features and DSP-based implementation of a robust fractional-order chaotic system.Based on the potential application prospect in secret communication,cryptography and other fields,we introduce a three-dimensional robust fractional-order chaotic system.Through theoretical analysis and numerical simulation,the dynamical properties of the fractional-order chaotic system are discussed.The important finding is that the control parameters can carry out amplitude modulation and position modulation on the state variables of the system.What's more,the dynamics remains constant with the variation of two systemic parameters.Consequently,this system can provide rich encoding keys for chaotic communication.Adomian decomposition method is used to solve fractional-order chaotic system,and it is verified on DSP-based platform,which lays a foundation for engineering application.(4)Research on synchronization of a fractional-order chaotic system.By considering the properties of amplitude and position modulation of the robust fractional-order,the partial projective synchronization and partial phase synchronization are proposed with linear control scheme.The coupling parameter range for synchronization is derived analytically.The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller.In addition,a finite-time synchronization scheme for robust fractional-order systems under disturbance is presented,and a finite-time synchronization controller's system design scheme is proposed.Numerical simulations are executed to confirm the theoretical analysis.(5)Research on image encryption algorithm based on chaotic system.The chaotic systems are widely used in secure communications and image encryption.In this dissertation,a color image encryption algorithm based on fractional-order system and three-channel Arnold transformation is proposed.A three-dimensional chaotic map is constructed by Chebyshev,Tent map and modulus operation as seed maps.And their three state output sequences are used for three Arnold matrix's parameters.R,G and B sub-image are scrambled parallelly.Then the permuted images are diffused dependently with each component by secret-key stream which are generated by a robust fractional-order chaotic system.Since the initial values of the three-dimensional chaotic map are related to image pixel gray value,and the initial values of the fractional-order system are also related to the SHA-256 hash value of the plaintext image,the algorithm can effectively resist the chosen-plaintext attack.The encryption system has large key space,good security and anti-attack capability because of the using the robust chaotic systems.