基于改进Adomian分解法的分数阶Rabinovich超混沌系统实验仿真
|
摘要
采用改进Adomian分解法对分数阶Rabinovich超混沌系统进行仿真。从系统单参数变化下的分岔图、复杂度C0数值仿真分析了分数阶Rabinovich超混沌系统从周期到混沌所具有的动力学行为,运用双参数变化下的复杂度研究了系统分岔空间的特点。仿真结果表明:分数阶混沌系统阶数q越大,系统复杂度越低。这种理论与仿真相结合的方法使得学生能深入理解了分数阶动力学系统,有效地提高了教学质量。
The improved Adomian decomposition method is used to simulate the fractional Rabinovich hyperchaotic system.The dynamic behavior of the fractional order Rabinovich hyperchaotic system from the periodic to chaotic is analyzed by the numerical simulation of the bifurcation diagram and C0 complexity under single parameter variation,and the characteristics of system bifurcation space are studied by using the complexity of two parameter changes.The simulation results show that the larger the order q of the fractional order chaotic system is,the lower the complexity of the system is.This method of combining theory with simulation enables students to understand the fractional order dynamics system deeply,which effectively improves teaching quality.
The improved Adomian decomposition method is used to simulate the fractional Rabinovich hyperchaotic system.The dynamic behavior of the fractional order Rabinovich hyperchaotic system from the periodic to chaotic is analyzed by the numerical simulation of the bifurcation diagram and C0 complexity under single parameter variation,and the characteristics of system bifurcation space are studied by using the complexity of two parameter changes.The simulation results show that the larger the order q of the fractional order chaotic system is,the lower the complexity of the system is.This method of combining theory with simulation enables students to understand the fractional order dynamics system deeply,which effectively improves teaching quality.
引文
[1] Hilfer R.Applications of fractional calculus in physics[M].New Jersey:World scientific,2001.
[2] Mandelbrt B B.The Fractal Geometry of Nature[M].New York:Freeman,1983.
[3] Lu J G.Nonlinear observer design to synchronize fractional-order chaotic system via a scalar transmitted signal[J].Physica A:Statistical Mechanics and its Applications,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,Li J,Chen G R.Chaos in the fractional order unified system andits synchronization[J].Chinese physics,2007,16(7):392-401.
[6] Bao Bocheng,Liu Zhong,Xu Jianping.New chaotic system and its hyperchaos generation[J].Journal of Systems Engineering and Electronics,2009,20(6):1179-1187.
[7]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):58-65.
[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):56-62.
[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,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]杨叶红,肖剑,马珍珍.一个新分数阶混沌系统的同步和控制[J].山东大学学报(理学版),2014,49(2):76-83,88.
[12]雷腾飞,胡庆玲,尹劲松,等.基于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.
[13] He Shaobo,Sun kehui,Mei Xiaoyong.Numerical analysis of a fractional-order chaotic system based on conformable fractionalorder derivative[J].European Physical Journal Plus,2017,132(1):36.
[14]薛雪,刘晓文,陈桂真,等.蔡氏混沌电路综合设计性实验[J].实验技术与管理,2017,34(6):44-49.
[15]闵富红,彭光娅,叶彪明,等.无感蔡氏电路混沌同步控制实验[J].实验技术与管理,2017,34(2):43-46,49.
[16]Li Yongjian,Yang Qigui,Pang Guoping.A hyperchaotic system from the Rabinovich system[J].Journal of Computational and Applied Mathematics,2010(1):101-113.
[2] Mandelbrt B B.The Fractal Geometry of Nature[M].New York:Freeman,1983.
[3] Lu J G.Nonlinear observer design to synchronize fractional-order chaotic system via a scalar transmitted signal[J].Physica A:Statistical Mechanics and its Applications,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,Li J,Chen G R.Chaos in the fractional order unified system andits synchronization[J].Chinese physics,2007,16(7):392-401.
[6] Bao Bocheng,Liu Zhong,Xu Jianping.New chaotic system and its hyperchaos generation[J].Journal of Systems Engineering and Electronics,2009,20(6):1179-1187.
[7]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):58-65.
[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):56-62.
[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,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]杨叶红,肖剑,马珍珍.一个新分数阶混沌系统的同步和控制[J].山东大学学报(理学版),2014,49(2):76-83,88.
[12]雷腾飞,胡庆玲,尹劲松,等.基于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.
[13] He Shaobo,Sun kehui,Mei Xiaoyong.Numerical analysis of a fractional-order chaotic system based on conformable fractionalorder derivative[J].European Physical Journal Plus,2017,132(1):36.
[14]薛雪,刘晓文,陈桂真,等.蔡氏混沌电路综合设计性实验[J].实验技术与管理,2017,34(6):44-49.
[15]闵富红,彭光娅,叶彪明,等.无感蔡氏电路混沌同步控制实验[J].实验技术与管理,2017,34(2):43-46,49.
[16]Li Yongjian,Yang Qigui,Pang Guoping.A hyperchaotic system from the Rabinovich system[J].Journal of Computational and Applied Mathematics,2010(1):101-113.