Research On Dynamics Of Fractional-order Chaotic System And Its Application In Image Encryption

Fractional-order chaotic system has complex dynamic characteristics and outstanding engineering application value,so it is widely used in communication science,physics,economics,biomedicine and other fields,and has aroused great interest of researchers in the field of synchronous control and information encryption.At the same time,the construction of fractional-order chaotic system which can produce special dynamic phenomena has become a research hotspot.For example,a system with hidden attractor,extremely hidden multistability and controllable variable-wing hyperchaotic attractor is constructed.However,at present,the relevant research is less or not comprehensive.Therefore,a series of new fractional-order chaotic systems are constructed in this paper.The specific work can be summarized as follows:(1)A new fractional-order chaotic system without equilibrium point is constructed.Through phase diagram,bifurcation diagram,Lyapunov exponent spectrum and complexity chaos diagram,the complex hidden dynamics of the system is analyzed theoretically and numerically.The state transition behavior of the system is analyzed by time series and phase diagram.Interestingly,although the system does not have equilibrium point,it can generate various types of coexisting hidden attractors and hidden extreme multistability after selecting appropriate parameters and initial values.The corresponding physical circuit is designed and the hardware test results are given.By comparing with the results of MATLAB numerical analysis software,the physical realizability of the system is verified,which can be applied in real life.(2)In the study of variable wing chaotic system,although some researchers have proposed that one-to-four wing chaotic system can be generated,the attractors are not all hyperchaotic,which is incomplete for the study of chaotic system dynamics.Therefore,based on the 3D Lü system,a new 4D fractional-order hyperchaotic system is proposed.One-to-four wing hyperchaotic attractors can be obtained by changing a single parameter.The complex and abundant dynamic behaviors of fractional-order chaotic system are analyzed by phase diagram,bifurcation diagram and Lyapunov exponent.For example,the coexisting attractor can be obtained by changing the parameter d or the order q,and the persistent hyperchaotic state and the constant Lyapunov exponent behavior can be obtained by analyzing the parameter k.In addition,we use SE and C0 algorithm to analyze the complexity of fractional chaotic system.The influence of order q on the system is studied.Through the hardware circuit experiment,the effectiveness and feasibility of the system are proved.(3)Based on the proposed fractional-order hyperchaotic system,chaotic sequences are applied to image encryption.A new encryption algorithm is proposed by combining scrambling and substitution,and setting system parameters and initial values as encryption keys.The reliability,validity and security of the encryption algorithm are analyzed in MATLAB.It mainly includes histogram,key sensitivity,neighbor pixel correlation and so on.The results show that the encryption scheme has strong key sensitivity,low correlation,and strong anti-cracking ability for statistical analysis.It shows that the color image encryption scheme has a good application prospect.