新的具有光滑二次函数混沌系统的构建与实现  

A new smooth quadratic chaotic system and its digital signal processing implementation

作　　者：刘扬正[1] 林长圣[1] 李心朝[1] 

机构地区：[1]南京工程学院非线性物理研究所,南京211167

出　　处：《物理学报》2011年第6期121-125,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:90405011);江苏省高等学校自然科学基金(批准号:07KJD120081);南京工程学院自然科学基金(批准号: KXJ07068)资助的课题~~

摘　　要：拓展和改变Lorenz混沌系统的非线性函数,构建一个新的具有光滑二次函数的自治混沌系统,系统包含3个系统变量乘积的非线性函数项和5个平衡点,详细讨论了平衡点的性质并计算了分形维数.利用分岔图和Lyapunov指数谱对系统随参数变化的情况进行分析后得出,系统会发生倍周期分岔.用数字信号处理芯片对混沌系统进行硬件实现,实验结果表明理论分析的正确性以及系统具有较为复杂的动力学行为.Developing and changing nonlinear function of Lorenz chaotic system, a new autonomous chaotic system is generated which contains three smooth quadratic terms of system variables and five equilibriums. The characteristics of five equilibriums are discussed and a fractal dimension is calculated. The features of chaotic system are analyzed in detail using bifurcation diagram and Lyapunov exponent. The period doubling bifurcation of the system can occus. The chaotic system is realized based on digital signal processing. Experimental result shows the effectiveness and feasibility of the theoretical analysis and verifies the behaviors of various attractors.

关 键 词：混沌系统 分岔图 LYAPUNOV指数 数字信号处理 

分 类 号：O415.5[理学—理论物理]