本文基于里兹—伽辽金法,将考虑几何非线性的一端固支一端夹支复合材料层合梁的控制方程简化为典型的Duffing方程;引入了Duffing-Van Der Pol系统,通过两种系统的分岔图说明了它们共同达到混沌时的参数值;通过广义投影同步法,实现了Duffing系统和Duffing-Van Der Pol系统的精确同步,得到了实现两种系统同步的控制器;分别将两种系统通过Matlab进行了数值仿真,得到了两种系统的同步误差曲线图、二维相图和三维相图,从而验证了混沌同步的准确性。
Abstract
Based on Ritz-Galerkin Method, the governing equations of composite beam with the clamped-fixed boundary conditions can be simplified to the typical formal of Duffing Equations when geometric nonlinear is taken into consideration. The Duffing-Van Der Pol System is introduced, and parameter values of two systems reaching the chaotic state commonly are obtained according to their bifurcation diagrams. The accurate synchronization among the Duffing System and the DVP System (short for Duffing-Van Der Pol) can be achieved by generalized projective synchronization method and their controller is also acquired. Finally, numerical analysis of chaotic synchronization is accomplished by Matlab and synchronous error curve diagrams, 2D-phase-trajectory diagrams, 3D-phase-trajectory diagrams can be gotten, these diagrams are used to verify the accuracy of chaotic synchronization.
关键词
复合材料 /
混沌同步 /
DVP系统 /
广义投影同步
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Key words
composite /
chaotic synchronization /
DVP system /
generalized projective synchronization method
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参考文献
[1] Liu Yang-Zheng,Jiang Chang-Sheng. Chaos switch-synchron- ization for a class of 4-D chaoticsystems[J]. Acta Physica Sinica, 2007(2).
[2] Maggio G,Rulkov N,Reggiani L. Pseudo-chaotic time hopping
for UWB impulse radio[J]. IEEE Trans on Circuit and System,
2001,48(12):1424-1434.
[3] Fridrich J,Goljan M. Protection of digital images using self embedding[EB/OL] http://Proc of IC IP99,1999.
[4] Pecora.L.M,Carroll.T.L. Synchronization in chaotic systems [J].Physical Review Letters, 1990,64(8):821-827.
[5] L.Kocarev,U.Parlitz. General Approach for Chaotic Synchroni-zation with Applications to Communication[J], Phys.Rev.Lett,1995(74),5028-5031.
[6] Pyragas.K. Experimental Control of Chaos by delayed
self-controlling feedback[M]. Phys.Lett.A, 1993(181),203.
[7] Mainieri.R,Rehacek.J. Projective synchronization in three-dimensional chaotic systems[J]. Phys.Rev.Lett,1999,82(15):3042-3045.
[8] Yan J P,Li C P. Generalized projective synchronization of a unifiedchaotic system[J]. Chaos Solitons and Fractals, 2005,26(4):1119-1124.
[9] Hu Manfeng,Xu Zhenyuan.Full state hybrid projective synchro-nization in continuous-time chaotic (hyperchaotic)systems[J]. Communications in Nonlinear Science and Numerical Simula-tion, 2008,13(2):456-464.
[10] 闵富红,王执铨. 两个四维混沌系统广义投影同步[J].物理学报,2007,56(11):6238-6244.
Min Fuhong,Wang Zhiquan. Generalized projective synchro-nization of two four-dimensional chaotic systems[J]. ACTA PHYSICA SINICA,2007,56(11):6238-6244.
[11] 闵富红,王执铨,史国生. 新型超混沌系统的改进自适应广义投影同步[J].系统仿真学报,2008,20(14):3785-3789.
Min Fuhong,Wang Zhiquan,Shi Guosheng.Adaptive Modified Generalized Projective Synchronization for New Hyper-cha-otic Systems[J]. Journal of System Simulation,2008,20(14):
3785-3789.
[12] 王宇野,许红珍. 异结构不确定混沌系统的广义投影同步[J]. 系统工程与电子技术,2010(2):355-358.
Wang Yuye, Xu Hongzhen.Generalized projective Synchron-ization between two different uncertain chaotic systems[J]. Systems Engineering and Electronics, 2010(2):355-358.
[13] 冯浩,杨洋. Chen系统和Liu系统的广义投影同步的电路仿真设计[J]. 河北北方学院学报(自然科学版),2013,29(5):14-17.
Feng Hao,Yang Yang.Circuit Simulation Design of Generali- zed Projective Synchronization of Chen System and Liu System[J]. Journal of Hebei North University(Natural Science
Edition),2013,29(5):14-17.
[14] 杨洋. 混沌系统全状态混合投影同步研究[D].石家庄:河北师范大学. 2007.
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脚注
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