Dynamic Research And FPGA Implementation Of Conservative Chaos

Chaos is a complex phenomenon produced by nonlinear systems.Chaotic systems have two important branches: conservative chaotic system and dissipative chaotic system.Conservative chaos has stronger internal randomness because it doesn’t produce attractors,so it is more widely used in image encryption and secure communication compared with dissipative chaotic system.Therefore,the study of conservative chaos has attracted extensive attention from scholars.However,due to the difficulty of constructing conservative chaotic system,few conservative chaotic systems have been discovered at present.In addition,the complexity of chaotic information is closely related to its dynamic characteristics in chaotic systems,which has more advantages and flexibility in engineering applications.Therefore,it is very necessary to study the complex conservative chaotic system.In this paper,several conservative chaotic systems with complex dynamic characteristics are constructed,and the corresponding theoretical analysis and experimental verification are completed.Specific research contents are as follows:1)A new complex chaotic system is established.With the variation of system’s parameters,the system has conservative and dissipative features respectively.The dynamic behaviors of the system are analyzed,and has the following three characteristics:(1)Selecting appropriate parameters,the system has conservative property,and it is a volume conservative chaotic system.Because of its unique nonlinear term has periodicity,so it can produce conservative extreme-multistablility phenomenon.(2)When the system is a dissipative chaotic system,it can generate self-excited and hidden chaotic attractors,which have abundant vortexes.(3)When the nonlinear term of the system is triangular wave function,chaotic sea and chaotic attractor can be produced as the change of system’s parameters.Finally,we design the corresponding circuit and verify the system on FPGA,and the results of the experiment are completely consistent with the numerical analysis results.2)We construct a non-Hamiltonian conservative hyperchaotic system.The conservatism of the system is judged by three methods: dissipation,existence of eternal points,sum of Lyapunov exponents and so on.There are two positive Lyapunov exponents in the system,which is a five-dimensional conservative hyperchaotic system.The phase orbit diagram,bifurcation diagram and time series are used to analyze the dynamic characteristics of the system.Finally,the digital circuit design of the system is designed on FPGA platform,and the results are obtained on oscilloscope to verify the correctness of theoretical analysis.3)The modified Sprott-A is a conservative chaotic system with infinitely many coexisting chaotic flows.The dynamical behaviors of the system are studied by using bifurcation diagram,Lyapunov exponents spectrum and phase orbital diagram.The system is a volumetric conservative chaotic system with the change of parameters,and the complex dynamic phenomenon of infinitely many chaotic flows can be found in the system.Finally,the circuit design of the system is completed,and the experimental results are obtained on oscilloscope to verify its feasibility.