一个切换Lorenz混沌系统的特性分析
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摘要
为使混沌系统更好地应用于工程实践,通过构造由2个子系统组成的切换Lorenz型混沌系统,分析子混沌系统和自动切换混沌系统的Lyapunov指数谱和分岔图,利用拓扑马蹄引理从理论上证明了切换混沌系统吸引子的存在性,基于模拟电路和数字电路2种实验手段实现了混沌系统,分析结果表明,在相同参数下,切换系统具有与子系统的不同的动力学特性,切换系统比子系统具有更大的混沌参数区间。实验结果与仿真结果完全一致,在理论和实验两方面证明了切换混沌系统的存在性。
In order to promote the application of chaotic systems in engineering practice,this paper presents a Lorenz-type switched system composed of two subsystems. The new chaotic system is analyzed with Lyapunov exponent spectrum and bifurcation diagram. To present a computer assisted verification of chaos,the switching system is also studied by utilizing topological horseshoe theory. Physical verification has also been done in two different methods with an analog electronic circuit and a digital electronic circuit,respectively. Numerical analysis shows that the switched system has a larger chaotic region than its subsystems and the dynamics characteristics much different from subsystems. It also shows that numerical and experimental results are matches very well. The existence of the chaotic attractors is proved in both theory and experiment.
In order to promote the application of chaotic systems in engineering practice,this paper presents a Lorenz-type switched system composed of two subsystems. The new chaotic system is analyzed with Lyapunov exponent spectrum and bifurcation diagram. To present a computer assisted verification of chaos,the switching system is also studied by utilizing topological horseshoe theory. Physical verification has also been done in two different methods with an analog electronic circuit and a digital electronic circuit,respectively. Numerical analysis shows that the switched system has a larger chaotic region than its subsystems and the dynamics characteristics much different from subsystems. It also shows that numerical and experimental results are matches very well. The existence of the chaotic attractors is proved in both theory and experiment.
引文
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[13]LI Qingdu,ZHANG Lang,YANG Fangyan.An Algorithm to Automaically Detect the Smale Horseshoes[J].Discret Dyn Nat Soc,2012(31):726-737.
[2]CHEN Guangrong,UETA T.Yet another chaotic attractor[J].International Journal of Bifurcation and Chaos,1999,9(7):1465-1466.
[3]蔡国梁,谭振梅,周维怀,等.一个新的混沌系统的动力学分析及混沌控制[J].物理学报,2007,56(11):6230-6237.CAI Guoliang,TAN zhengmei,ZHOU Weihuai,et al.Dynamical analysis of a new chaotic system and its chaotic control[J].Acta Phys Sin,2007,56(11):6230-6237.
[4]黄沄,罗小华,张鹏.一种新的具有光滑二次函数多涡卷混沌系统及其FPGA实现[J].重庆邮电大学学报:自然科学版,2012,24(4):479-482.HUANg Yun,LUO Xiaohua,ZHANG Peng.A novel smooth quadratic multi-scroll chaotic system and its implementation based on FPGA[J].Journal of Chongqing University of Post and Telecommunications:Natural Science Edition,2012,24(4):479-482.
[5]吴淑花,刘振永,张若洵,等.一个新三维系统的电路实现及其混沌控制[J].重庆邮电大学学报:自然科学版,2012,24(4):473-478.WU Shuhua,LIU Zhenyong,ZHANG Ruoxun,et al.Circuit simulation of a new three-dimensional chaotic system and its chaotic control[J],Journal of Chongqing University of Post and Telecommunications:Natural Science Edition,2012,24(4):473-478.
[6]曹学鹏,吕毅博,黄婷婷,等.不同混沌调制方式在基于超宽带系统的体内信道下的性能表现[J].重庆邮电大学学报:自然科学版,2016,28(1):72-77.CAO Xuepeng,LU Yibo,HUANG Tingting,et al.Performance of different DCSK schemes over the UWB inbody channel[J].Journal of Chongqing University of Post and Telecommunications:Natural Science Edition,2016,28(1):72-77.
[7]WANG Guangyi,BAO Xulei,WANG Zhonglin.Design and FPGA implementation of a new hyperchaotic system[J].Chinese physics B,2008,17(10):3596-3602.
[8]ZHANG Yajun,WANG Cuiping,WANG Guangyi,et al.Design and experimental confirmation of a Novel switched Hyperchaotic system[J].The Journal of China Universities of Posts and Telecommunications,2009,16(2):128-133.
[9]刘扬正,姜长生,林长圣,等.一类切换混沌系统的实现[J].物理学报,2007,56(6):3107-3112.LIU Yangzheng,JIANG Changsheng,LIN changsheng,et al.A class of switchable 3D chaotic systems[J].Acta Phys Sin,2007,56(6):3107-3112.
[10]王忠林,黄娜.一个自动切换混沌系统的设计与FPGA实现[J].中国海洋大学学报:自然科学版,2010,40(1):111-114.WANG Zhonglin,HUANG Na.Design and FPGA implementation of an automatism switch chaotic system[J].Periodical of Ocean University of China:Natural Science Edition,2010,40(1):111-114.
[11]MISCHAIKOW K,MROZEK M.Chaos in the Lorenz Equations:A Computer-Assisted Proof[J].Butt Am Math Soc,1995(32):66-72.
[12]YANG Xiaosong,LI Qingdu.Existence of horseshoes in a foodweb model[J].Int J Bifur Chaos,2004(14):1847-1852.
[13]LI Qingdu,ZHANG Lang,YANG Fangyan.An Algorithm to Automaically Detect the Smale Horseshoes[J].Discret Dyn Nat Soc,2012(31):726-737.