Analysis And FPGA Design Of(Conservative) Chaotic Systems

Nonlinear science is honored as the third scientific revolution after quantum mechanics and relativity in the 20th century,and chaos theory and its application are important parts of nonlinear science.Due to the extreme sensitivity of chaotic system to initial conditions,making chaotic system has potential application value in the fields of image encryption and communication security,which has aroused the interest of domestic and foreign scholars.The research work in this paper includes the analysis of chaotic system,hardware implementation,image encryption and synchronization.1.This paper proposes a new four-dimensional chaotic system,called system Ⅰ.The dynamic characteristics of system Ⅰ is analyzed from initial value sensitivity,dissipation and symmetry,stability of equilibrium points,Lyapunov exponents,bifurcation diagram,Poincare map and so on.Designing the experimental circuit of the system Ⅰ,the experimental results show that the simulation results are consistent with the numerical analyses,thus the existence and realizability of the chaotic attractor of the system Ⅰ are verified from the physical level.Furthermore,the system Ⅰ is designed and implemented by FPGA,and found that the result of FPGA is consistent with the result of circuit simulation and numerical analysis,it verifies that the hardware of the system Ⅰ is feasible.In addition,the fractional system I’ based on System Ⅰ is analyzed,and the FPGA is designed and implemented.2.Based on system Ⅰ,a new four－dimensional chaotie system is eonstructed,which is called system Ⅱ.The dynamic characteristics of system Ⅱ are analyzed,including the stability of equilibrium point,Poincare map and boundary estimation.At the same time,the circuit design of the system Ⅱ is carried out,and the simulation results show that the experimental results are consistent with the numerical results.Moreover,system Ⅱ is designed and implemented by FPGA,it verifies that the hardware of the system Ⅱ is feasible.3.Fractional order system I’proposed in this paper and a four-dimensional autonomous dynamical conservative chaotic system proposed by Cang et al are used for digital image encryption respectively,and the analysis results of encryption algorithm security performance are given.4.Based on the above work,a synchronization controller with different structures for four-dimensional chaotic systems Ⅰ and Ⅱ is designed in this paper,based on the theoretical analysis and numerical simulation of the synchronization controller,the hardware implementation of the synchronization system is realized by FPGA,it is found that the hardware implementation results are consistent with the theoretical analyses and numerical simulation results,which shows that the synchronization controller is effective and feasible.