Modeling And Analysis Of Complex Chaotic System And Design Of Pseudo-random Number Generator

Chaotic systems have several significant properties including initial value sensitivity,broadband,white-noise-like.Design and analysis of chaotic systems with complicated dynamics behaviors have become one of challenging and practical research topic due to their potential applications in the communication encryption.Chaos occurs in three different types of systems:(I)dissipative chaotic sytem;(II)conservative chaotic system;(III)quantum systems.In nonlinear system,hyperchaotic systems are more complicated than ordinary chaotic system since those system have at least two positive Lyapunov exponents implying chaotic flows stretching in multi-dimension.For conservative chaos,besides the general properties of chaos,there exist other properties,such as strong ergodicity,volume-conserving and constant energy.More importantly,for these conservative systems,there is no chaotic attractor,and different initial conditions lead to different dynamics,which gives the conservative chaotic flows distinct advantages over dissipative chaotic systems and so are used for information security.This paper mainly studies the dissipative hyperchaotic systems and high-dimensional conservative chaotic systems.The research contents are as follows:1.A new four-dimensional hyperchaotic system was proposed and the influence of parameter variation on the dynamic behavior of the system is analyzed in detail using phase diagram,Lyapunov exponent spectrum and the bifurcation diagram.In addition,topological horseshoe theory is used to proved the existence of hyperchaotic flows in the strictly mathematical sense.2.Lyapunov stability theory and optimization method are used to further analyze the ultimate boundary of the proposed 4D hyperchaotic system,which plays an important role in the study of the qualitative behavior of chaotic systems.3.Based on the generalized Hamiltonian system we proposed a general modeling method to design a class of Hamiltonian Conservative Chaotic Systems,which is employed to develop a few 4 dementional conservative chaotic systems and 5 dementional conservative hyper-chaotic system.4.By introducing trigonometric functions in a 4D conservative chaotic system,infinite1 D and 4D chaotic orbits,”parallel HCCS”,were observed in various sections of state space.Besides,the multistability is obtained,which means infinitely many scrolls depending on various initial values,can be found in the proposed systems5.The proposed HCCS is characterized by its strong pseudo-randomness in terms of LE values and nonattractive equilibrium points.Pseudo-randomness is confirmed following National Institute of Standards and Technology statistic test(NIST tests).In addition,Field programmable Gate Array technique was used to design pseudo-random number generator.