分数阶Qi混沌系统的动力学分析及DSP实现
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摘要
针对一类分数阶Qi混沌系统,运用分数阶微分常用的方法——Adomian分解法,从分数阶Qi系统的分岔图、SE复杂度、C0复杂度、混沌相图等数值仿真分析了0.95阶次Qi混沌系统复杂的动力学特性.基于Adomian分解法,采用高频率运算数字芯片TMS320F28335设计程序以及外围的基本硬件电路,实现了分数阶Qi混沌系统.通过示波器得出DSP数字电路输出结果与理论仿真结果具有一致性,从DSP实现方面揭示了分数阶Qi系统的混沌的存在性.
The fractional-order Qi chaotic system based on decomposition method of Adomian is studied in this paper. The complicated dynamic properties of 0.95 order Qi chaotic system are analyzed via the numerical simulation of fractional-order Qi bifurcation diagram, SE complexity, C0 complexity and chaotic phase space. And the fractional-order Qi chaotic system is implemented by means of TMS320 F28335, a high frequency digital chip which is used to design procedure as well as the peripheral hardware circuit. The experimental results through the oscilloscope that the result of DSP digital circuit output has consistency with the theoretical simulation result, which reveals the existence of fractional-order Qi chaotic system from the implement of the DSP(Digital Signal Processor).
The fractional-order Qi chaotic system based on decomposition method of Adomian is studied in this paper. The complicated dynamic properties of 0.95 order Qi chaotic system are analyzed via the numerical simulation of fractional-order Qi bifurcation diagram, SE complexity, C0 complexity and chaotic phase space. And the fractional-order Qi chaotic system is implemented by means of TMS320 F28335, a high frequency digital chip which is used to design procedure as well as the peripheral hardware circuit. The experimental results through the oscilloscope that the result of DSP digital circuit output has consistency with the theoretical simulation result, which reveals the existence of fractional-order Qi chaotic system from the implement of the DSP(Digital Signal Processor).
引文
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[3]Lu J G.Nonlinear observer design to synchronize fractional-order chaotic system via a scalar transmitted signal[J].Physica A,2006,359:107-118.
[4]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.
[5]Wu X J.Chaos in the fractional order unified system andits synchronization[J].Chinese Phys,2007,16(7):392-401.
[6]雷腾飞,陈恒,尹劲松,等.分数阶LV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.
[7]Bao B C,Liu Z,Xu J P.New chaotic system and its hyperchaos generation[J].J Systems Eng Elect,2009,20(6):1179-1187.
[8]刘崇新.一个超混沌系统及其分数阶电路仿真实验[J].物理学报,2007,56(12):6865-6873.
[9]Yuan L G,Yang Q G.Parameter identification and synchronization of fractional-order chaotic systems[J].Commun Nonlinear Sci,2012,17:305-316.
[10]Podlubny I.Fractional differential equations[J].New York:Academic Press,1999:21-25.
[11]Li C P,Deng W H.Remarks on fractions derivatives[J].Appl Math Comput,2007,187:777-784.
[12]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.
[13]薛薇,肖慧,徐进康,等.一个分数阶超混沌系统及其在图像加密中的应用[J].天津科技大学学报(自然科学版),2015,30(5):67-71.
[14]陈恒,雷腾飞,王震,等.分数阶Lorenz超混沌系统的动力学分析与电路设计[J].河南师范大学学报(自然科学版),2016,44(1):59-63.
[15]杨志宏,屈双惠,马志春,等.一类分数阶四翼混沌系统的动力学特性及其多元电路实现[J].华中师范大学学报(自然科学版),2016,50(5):665-671.
[16]雷腾飞,胡庆玲,尹劲松.基Adomian分解法的分数阶Chen混沌系统的动力学分析与DSP实现[J].曲阜师范大学学报(自然科学版),2016,42(3):76-82.
[17]Qi G Y,Chen G Y,Wyk M A,et al.A four-wing chaotic attractor generated form a new 3-D quadratic autonomous system[J].Chaos Soliton Fract,2008,28(3):705-721.
[18]Wang Z,Lei T F,Xi X J,et al.Fractional control and generalized synchronization for a nonlinear electromechanical chaotic system and its circuit simulation with Multisim[J].Turk J Electr Eng Co,2016,24(3):1502-1515.