CAJ | 학술논문

在经典三维 Lorenz 系统的基础上,增加一个非线性控制器,构造了一个新的四维超混沌 Lorenz 系统.通过数值计算,模拟分析了新系统的分岔图,Lyapunov 指数随控制参数的变化,超混沌吸引子的相图,求出系统的 Lyapunov 指数及其吸引子分形维数.结果显示,通过改变新引入的非线性控制器的控制参数,可以使超混沌 Lorenz 系统分别呈现超混沌、混沌以及周期、拟周期等动力学行为.根据新 Lorenz 系统的状态方程,设计了与之相对应的实验电路,并在示波器中观察到电路系统的动力学行为,该结果与数值仿真结果基本吻合.将系统应用于图像加密,模拟实验结果表明,该系统能产生具有良好密码学特性的伪随机序列.
재경전삼유 Lorenz 계통적기출상,증가일개비선성공제기,구조료일개신적사유초혼돈 Lorenz 계통.통과수치계산,모의분석료신계통적분차도,Lyapunov 지수수공제삼수적변화,초혼돈흡인자적상도,구출계통적 Lyapunov 지수급기흡인자분형유수.결과현시,통과개변신인입적비선성공제기적공제삼수,가이사초혼돈 Lorenz 계통분별정현초혼돈、혼돈이급주기、의주기등동역학행위.근거신 Lorenz 계통적상태방정,설계료여지상대응적실험전로,병재시파기중관찰도전로계통적동역학행위,해결과여수치방진결과기본문합.장계통응용우도상가밀,모의실험결과표명,해계통능산생구유량호밀마학특성적위수궤서렬.
@@@@On the basis of the classical three-dimensional Lorenz system, this paper increases a nonlinear controller to construct a new four-dimensional hyperchaotic Lorenz system. The dynamics of the new system conduct are studied by bifurcation analysis, Lyapunov exponent spectrum and phase chart fractal dimension. Numerical simulations show that the hyperchaotic Lorenz system can render different dynamics behavior of hyperchaos, chaos, periodicity and quasi-periodicity. Furthermore, a corre-sponding experiment circuit is designed, the mechanics conduct of the electrical system through a oscillogram is observed, the result basically unanimous with the numerical simulation results. Finally, the new hyperchaotic system is applied to image encryption, and computer simulation experiments confirm that the new hyperchaotic system can produce good cryptographic properties of pseudo-random sequence.