1、 l :2008-08-31 “: S “(BZXYQNLG200501); L/ “(BZXYSYXM200702)Te: (1970- ), 3, =, V,1V YEDA/ .Email:, cI|:1671-9352(2008)12-0093-04FPGAB“d !9 LC王忠林1 ,姚福安2 ,李祥峰2(1. 0 S“, 256603;2. v e S, 6 2250061)K1:提出了一种基于FPGA新的实现超混沌系统的方法,利用Matlab/Simulink中的DSPBuilder工具箱设计了一个电路模型,仿真成功后,把模型文件转换成VHDL代码程序,对VHDL语言代码进行编译、
2、仿真、配置后,用Quartus II下载到FPGA硬件电路中.结果表明新方法简单方便且能有效地产生超混沌吸引子.实验结果与仿真结果完全一致.1oM:混沌系统;Lorenz系统;Lyapunov指数谱ms |:TN914.42 DS :ADesign and realization of a hyperchaotic system based FPGAWANG Zhong-lin1 , YAO Fu-an2 , LIXiang-feng2(1.Department of Physics and Electronics, Binzhou University, Binzhou 256603, Sh
3、andong, Chian;2.School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China)Abstract:A novel method was adopted to design a hyperchaotic system Generator, based on a hyperchaotic system and imple-mented in FPGA.This methodwas based on theMatlab/Simulink, Altera Quar
4、tus II and DSP Builder.The hyperchaotic systemwas built by Altera DSP Builder, which is embedded into the Matlab/Simulink as a toolbox.After successful simulation of thismodel, theVHDL code was generated automatically.Then this code could be complied, simulated, configured and download bythe AlteraQ
5、uartus II.The research results indicated that this new method is not only simple and convenient but also effective toprecisely producea hyperchaotic system.It showed good agreement between system simulations and experimental results.Key words:hyperchaotic system;Lorenz system;Lyapunov exponents spec
6、trum0 引言M1,“d 22 Lyapunov ,MEZ_ s , 。“ V4 YF 。yN,| 5B1 5。 Y、F 5, 3 B1o/ , B 3“dZE。1Chen QeZE LCB “d 1 , 3 3 v 2-7 。1979 MRossler OEBQ4 Q8 。/ LC1 E 32ZE, E LC/D 4-6 。D 7,9sYZEFPGA LC f 0 3。4 B LC / 0ZE。Matlab/Simulink,DSP BuilderLC “d_,SignalCompiler VHDL ,/FPGAq , FPGA L VI ?, P !9 EMd 。ZE !9 3/ 0,
7、LT_T B。1 超混沌模型及其吸引子2004 MLiu4 1“d10 , 43 12 Vol.43 No.12 v ( )Journal of Shandong University(Natural Science) 2008 M12 Dec.2008 Z:x =a(y -x),y =bx-xz ,z =x2 -cz 。(1)a =10,b =40,c=2 H,“d(1) 。“d(1) Q eEB“d,BZ9F BdLyz ,=、 ZM 9M, Z BQ e w ,i9F B1wBsZ 1“d:x =-ax +(y +1)z ,y =by -xz ,z =xy -cz -gw ,w =-dx
8、。(2)“d(2) 0M bW 4, Oc3dL, A1Hq。 “dM1,“d(2) BdL,yN ,9 _TV a =10,b =2.5,c=4,d =0.25,g =2 H,“d(2)r , 09 _m m1 U。m1 0M g(a)x-y ;(b)x-z ;(c)x -u ;(d)y -z ;(e)y -u ;(f)z -u Fig.1 Phase portraits of chaotic attractors of system(a)x-y plane;(b)x -z plane;(c)y -z plane;(d)x -y plane;(e)x -z plane;(f)y-z plan
9、e2 超混沌的基本特性 p“d(2) ,“d(1) 7 M x , y, z , u, O“d(2)P 0。 V“dS(0,0,0,0)。S “d(2)B 。 S , T(2)L,Jaco-bian +:1 =0.012 4, 2 =2.5, 3 =-9.991 6,4 =-4.0208。 12 L ,7345 L ,yN, S1(0,0,0,0)B。“d B “d,Z(2)V = x x+ y y + z z + u u =-(a -e +c)=-11.5,t H,c“dEL 8 ( q-11.5 l 011 。 0M #ELWC4N t ,i qMs ,7Lyapunov EL4N 。“d
10、Lya-punov LE1 =0.467 5, LE2 =0.015 2, LE3 =0,LE4 =-11.951 2, ! Hq,2Lyapunov ,iB0, (+, +,0, -),N H“dLyapunov DL =3.04,NV, s “d。3 Lyapunov指数谱与分岔图“d1 + VYV Lyapunov sm s。bM H,Lyapunov M ysm m2 U。N H, a =10, c=4, d =94 v ( )43 0.25,g =2, Lyapunov s H, LE4 0,LE2 =0,LE4 LE2 0,LE3 =0,LE4 .Liu“ds# L J . ,2006,55(10):5061-5069. 111 , g.Lorenz“dB s、 e M .: S,2003.(编辑:孙培芹)96 v ( )43
