分数阶Lorenz超混沌系统的动力学分析与电路设计
|
摘要
针对一类分数阶Lorenz超混沌系统,分别从系统的分岔图、Lyapunov指数图和吸引子相图等角度分析与验证了分数阶Lorenz超混沌系统丰富的动力学行为.同时基于整数阶混沌电路的设计策略,设计了模拟电路,实现了分数阶Lorenz超混沌系统.最后,通过示波器观察到电路仿真结果与数值仿真结果具有一致性,从而揭示了分数阶超混沌系统的可实现性,也表明了分数阶混沌电路的正确性.
This paper,for a fractional order Lorenz hyperchaotic system,is to analyze and verify the fractional order Lorenz hyperchaotic system dynamics behavior based on such numerical simulations as the bifurcation diagram,the Lyapunov index figure and attractor phase diagram.The analog circuit was designed and the fractional order Lorenz chaotic system is realized on the basis of integer order chaotic circuit design strategy.Finally,the consistence of numerical simulation results and circuit simulation results observed through the oscilloscope reveals the realizability of hyperchaotic system of fractional order,and the validity of the fractional order chaotic circuit.
This paper,for a fractional order Lorenz hyperchaotic system,is to analyze and verify the fractional order Lorenz hyperchaotic system dynamics behavior based on such numerical simulations as the bifurcation diagram,the Lyapunov index figure and attractor phase diagram.The analog circuit was designed and the fractional order Lorenz chaotic system is realized on the basis of integer order chaotic circuit design strategy.Finally,the consistence of numerical simulation results and circuit simulation results observed through the oscilloscope reveals the realizability of hyperchaotic system of fractional order,and the validity of the fractional order chaotic circuit.
引文
[1]LORENZ E N.Deterministic nonperiodic flow[J].J Atmos.Science,1963,20:130-141.
[2]CHEN G,UETA T.Yet another chaotic attractor[J].International Journal of Bifurcation and chaos,1999,9(7):1465-1466.
[3]LU J H,CHEN G R.A new chaotic attractor coined[J].International Journal of Bifurcation and chaos,2002,12(3):659-661.
[4]康宁,孔祥星,侯振挺等两个重要混沌系统的不等价性证明[J].系统科学与数学,2013,33(9):1113-1118.
[5]LU J G.Nonlinear observer design to synchronize fractional-order chaotic system via a scalar transmitted signal[J].Physica A,2006,359:107-118.
[6]WU X J.Chaos in the fractional order unified system and its synchronization[J].Chinese physics,2007,16(7):392-401.
[7]崔力,欧青立,徐兰霞.分数阶Lorenz超混沌系统及其电路仿真[J].电子测量技术,2011,23(5):13-16.
[8]LIU F,TURMER I,ANH V.An Unstruetured Mesh Finite Volume Method for Model ling Saltwater Intrusionin to Coastal Aquifers[J].Korean J Comput&Appl Iath,2002,9(2):391-07.
[9]马铁东,江伟波,浮洁,等.一类分数阶混沌系统的自适应同步[J].物理学报,2012,61(16):90-95.
[10]王震,孙卫.分数阶Chen混沌系统同步及Multisim电路仿真[J],计算机工程与科学,2012,34(1):187-192.
[11]闵富红,余杨,葛曹君.超混沌分数阶LV系统电路实验与追踪控制[J].物理学报,2009,58(3):1456-1460.
[12]梁松,张云雷,吴然超.分数阶多时滞混沌系统的同步[J].河南师范大学学报(自然科学版),2015,43(2):25-29.
[13]贾红艳,陈增强,薛薇.分数阶Lorenz系统的分析及电路实现[J].物理学报,2013,62(14):140503-1-7.
[14]雷腾飞,陈恒,尹劲松,等.分数阶Lü混沌系统的分析与电路模拟[J],曲阜师范大学学报(自然科学版),2015,41(2):35-41.
[15]陈恒,雷腾飞,王震,等.分数阶Chen混沌系统的动力学分析与电路实现[J],河北师范大学学报(自然科学版),2015,39(3):208-215.
[16]王发强,刘崇新.分数阶临界混沌系统及电路实验的研究[J].物理学报,2006,55(8):392-3927.
[17]王兴元,王明军.超混沌Lorenz系统[J].物理学报,2007,56(9):5136-5141.
[18]王明军,王兴元.分数阶Newton-Leipnik系统的动力学分析[J].物理学报,2010,59(3):1583-1591.
[2]CHEN G,UETA T.Yet another chaotic attractor[J].International Journal of Bifurcation and chaos,1999,9(7):1465-1466.
[3]LU J H,CHEN G R.A new chaotic attractor coined[J].International Journal of Bifurcation and chaos,2002,12(3):659-661.
[4]康宁,孔祥星,侯振挺等两个重要混沌系统的不等价性证明[J].系统科学与数学,2013,33(9):1113-1118.
[5]LU J G.Nonlinear observer design to synchronize fractional-order chaotic system via a scalar transmitted signal[J].Physica A,2006,359:107-118.
[6]WU X J.Chaos in the fractional order unified system and its synchronization[J].Chinese physics,2007,16(7):392-401.
[7]崔力,欧青立,徐兰霞.分数阶Lorenz超混沌系统及其电路仿真[J].电子测量技术,2011,23(5):13-16.
[8]LIU F,TURMER I,ANH V.An Unstruetured Mesh Finite Volume Method for Model ling Saltwater Intrusionin to Coastal Aquifers[J].Korean J Comput&Appl Iath,2002,9(2):391-07.
[9]马铁东,江伟波,浮洁,等.一类分数阶混沌系统的自适应同步[J].物理学报,2012,61(16):90-95.
[10]王震,孙卫.分数阶Chen混沌系统同步及Multisim电路仿真[J],计算机工程与科学,2012,34(1):187-192.
[11]闵富红,余杨,葛曹君.超混沌分数阶LV系统电路实验与追踪控制[J].物理学报,2009,58(3):1456-1460.
[12]梁松,张云雷,吴然超.分数阶多时滞混沌系统的同步[J].河南师范大学学报(自然科学版),2015,43(2):25-29.
[13]贾红艳,陈增强,薛薇.分数阶Lorenz系统的分析及电路实现[J].物理学报,2013,62(14):140503-1-7.
[14]雷腾飞,陈恒,尹劲松,等.分数阶Lü混沌系统的分析与电路模拟[J],曲阜师范大学学报(自然科学版),2015,41(2):35-41.
[15]陈恒,雷腾飞,王震,等.分数阶Chen混沌系统的动力学分析与电路实现[J],河北师范大学学报(自然科学版),2015,39(3):208-215.
[16]王发强,刘崇新.分数阶临界混沌系统及电路实验的研究[J].物理学报,2006,55(8):392-3927.
[17]王兴元,王明军.超混沌Lorenz系统[J].物理学报,2007,56(9):5136-5141.
[18]王明军,王兴元.分数阶Newton-Leipnik系统的动力学分析[J].物理学报,2010,59(3):1583-1591.