基于Adomian分解法的分数阶混沌系统的动力学分析与电路实现
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摘要
针对一类分数阶混沌系统,运用分数阶微分常用的方法——Adomian分解法,从分数阶混沌系统的混沌相图、分岔图、最大Lyapunov指数(MLE)、复杂度SE与复杂度C_0以及空间分岔图等数值仿真分析了0.9阶次混沌系统复杂的动力学特性。同时,基于频率分析法,设计出了0.90～0.99阶次的分数阶电路模块并用电路实现了0.96阶混沌系统。最后,观测示波器电路实验结果与理论分析结果相一致,从而进一步揭示了此类分数阶混沌系统的可实现性与混沌特性。
Fractional-order chaotic system is studied based on decomposition method of Adomian. The rich characteristics of 0.9 order chaotic system are analyzed and validated according to the numerical simulation analysis of the system bifurcation diagram of the system,SE complexity,C0 complexity and Bifurcation space. At the same time,based on the frequency analysis method,0.9 ～ 0.99 order circuit module is designed and 0.96 order chaotic systems by circuit implementation. The experimental results are consistent with the numerical calculation through the oscilloscope observation,which reveals the abundant dynamics characteristic and realization of the chaotic system to the further.
Fractional-order chaotic system is studied based on decomposition method of Adomian. The rich characteristics of 0.9 order chaotic system are analyzed and validated according to the numerical simulation analysis of the system bifurcation diagram of the system,SE complexity,C0 complexity and Bifurcation space. At the same time,based on the frequency analysis method,0.9 ～ 0.99 order circuit module is designed and 0.96 order chaotic systems by circuit implementation. The experimental results are consistent with the numerical calculation through the oscilloscope observation,which reveals the abundant dynamics characteristic and realization of the chaotic system to the further.
引文
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[2]Mandelbrt B B.The Fractal Geometry of Nature[M].New York:Freeman,1983:59-60.
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[5]仲启龙,邵永辉,郑永爱.基于TS模型的分数阶混沌系统同步[J].扬州大学学报(自然科学版),2014,17(3):46-49.
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[9]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.
[10]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.
[11]贺少波,孙克辉,王会海.分数阶混沌系统的Adomian分解法求解及其复杂性分析[J].物理学报,2014,63(3):030502.
[12]邵书义,闵富红,马美玲,等.分数阶Chua’s系统错位同步无感模块化电路实现及应用[J].物理学报,2013,62(13):130504-1-8.
[13]孔德彭,陈安妮,周一飞,等.基于FPGA技术的WSN节点混沌保密通信设计[J].传感技术学报,2015,28(4):557-562.
[14]郑丹丹,张涛.基于混沌理论的涡街微弱信号检测方法研究[J].传感技术学报,2007,20(5):1103-1108.
[15]李春来,禹思敏,罗晓曙.一个新的混沌系统的构建与实现[J].物理学报,2012,61(11):127-136.
[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(8):3922-3927.
[2]Mandelbrt B B.The Fractal Geometry of Nature[M].New York:Freeman,1983:59-60.
[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]仲启龙,邵永辉,郑永爱.基于TS模型的分数阶混沌系统同步[J].扬州大学学报(自然科学版),2014,17(3):46-49.
[6]Podlubny I.Fractional Differential Equations[M].Academic Press:New York,1999:32-67.
[7]Li C P,Deng W H.Remarks on Fractions Derivatives[J].Applied Mathematics and Computation,2007,187:777-784.
[8]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.
[9]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.
[10]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.
[11]贺少波,孙克辉,王会海.分数阶混沌系统的Adomian分解法求解及其复杂性分析[J].物理学报,2014,63(3):030502.
[12]邵书义,闵富红,马美玲,等.分数阶Chua’s系统错位同步无感模块化电路实现及应用[J].物理学报,2013,62(13):130504-1-8.
[13]孔德彭,陈安妮,周一飞,等.基于FPGA技术的WSN节点混沌保密通信设计[J].传感技术学报,2015,28(4):557-562.
[14]郑丹丹,张涛.基于混沌理论的涡街微弱信号检测方法研究[J].传感技术学报,2007,20(5):1103-1108.
[15]李春来,禹思敏,罗晓曙.一个新的混沌系统的构建与实现[J].物理学报,2012,61(11):127-136.
[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(8):3922-3927.