{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Define the function that w ill display cobweb plots." }}{PARA 0 "" 0 "" {TEXT -1 125 "f will be t he function, n will iterate the given point (start) n times, domain an d range will specify the region of the plot." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 463 "cobweb := proc(f,n,start,domain,range)\n local a , i, s, gra, gpl, fpl, ipl;\n a := evalf(start);\n gra := [[a,f( a)],[f(a)-a,0]]; \n for i to n do a := f(a); \n gra := gra,[[a, a],[0,f(a)-a]],[[a,f(a)],[f(a)-a,0]];\n od:\n gpl := arrow([gra] ,shape=arrow,color=red,head_length=0.02,head_width=0.02);\n fpl := \+ plot(f,domain,color=black);\n ipl := plot(x->x,domain,color=blue); \n print(plots[display]([gpl,fpl,ipl],view=[domain,range]));\n e nd:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Define the standard Quadra tic Function and display the required cobweb plot." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "T:=x-> piecewise(x>=0 and x<1/2,2*x,x>=1/2 \+ and x<=1,2-2*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TGf*6#%\"xG6\" 6$%)operatorG%&arrowGF(-%*piecewiseG6&31\"\"!9$2F2#\"\"\"\"\"#,$F2F631 F4F21F2F5,&F6F5*&F6F5F2F5!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "cobweb(T,15,0.757,0..1,0..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 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bv7$F\\v$\"++++!=#F2F8F<-F$6&7$Fbv7$Fhu$\"$;%F*7%7$Fev$\"++++gRF2F]w7$ FhvFbwF8F<-F$6&7$F]w7$F^wF^w7%7$Fbw$\"++++gUF2Fhw7$Fbw$\"++++gSF2F8F<- F$6&7$Fhw7$F^w$\"$K)F*7%7$F^x$\"++++?\")F2Fcx7$F[xFhxF8F<-F$6&7$Fcx7$F dxFdx7%7$Fhx$\"++++?%)F2F^y7$Fhx$\"++++?#)F2F8F<-F$6&7$F^y7$Fdx$\"$O$F *7%7$Fay$\"++++gNF2Fiy7$FdyF^zF8F<-F$6&7$Fiy7$FjyFjy7%7$F^z$\"++++gKF2 Fdz7$F^z$\"++++gMF2F8F<-F$6&7$Fdz7$Fjy$\"$s'F*7%7$Fgz$\"++++?lF2F_[l7$ FjzFd[lF8F<-F$6&7$F_[l7$F`[lF`[l7%7$Fd[l$\"++++?oF2Fj[l7$Fd[l$\"++++?m F2F8F<-F$6&7$Fj[l7$F`[l$\"$c'F*7%7$F]\\l$\"++++gnF2Fe\\l7$F`\\lFj\\lF8 F<-F$6&7$Fe\\l7$Ff\\lFf\\l7%7$Fj\\l$\"++++gkF2F`]l7$Fj\\l$\"++++gmF2F8 F<-F$6&7$F`]l7$Ff\\l$\"$)oF*7%7$Fc]l$\"++++!o'F2F[^l7$Ff]lF`^lF8F<-F$6 &7$F[^l7$F\\^lF\\^l7%7$F`^l$\"++++!)pF2Ff^l7$F`^l$\"++++!y'F2F8F<-F$6& 7$Ff^l7$F\\^l$\"$C'F*7%7$Fi^l$\"++++SkF2Fa_l7$F\\_lFf_lF8F<-F$6&7$Fa_l 7$Fb_lFb_l7%7$Ff_l$\"++++ShF2F\\`l7$Ff_l$\"++++SjF2F8F<-F$6&7$F\\`l7$F b_l$\"$_(F*7%7$F_`l$\"++++?tF2Fg`l7$Fb`lF\\alF8F<-F$6&7$Fg`l7$Fh`lFh`l 7%7$F\\al$\"++++?wF2Fbal7$F\\al$\"++++?uF2F8F<-F$6$7U7$FCFC7$$\"3emmm; arz@!#>$\"39LLLL3VfVFabl7$$\"3[LL$e9ui2%Fabl$\"3'pmm;H[D:)Fabl7$$\"3nm mm\"z_\"4iFabl$\"3LLLLe0$=C\"!#=7$$\"3[mmmT&phN)Fabl$\"3ILLL3RBr;F^cl7 $$\"3CLLe*=)H\\5F^cl$\"3Ymm;zjf)4#F^cl7$$\"3gmm\"z/3uC\"F^cl$\"3=LL$e4 ;[\\#F^cl7$$\"3%)***\\7LRDX\"F^cl$\"3p****\\i'y]!HF^cl7$$\"3]mm\"zR'ok ;F^cl$\"3,LL$ezs$HLF^cl7$$\"3w***\\i5`h(=F^cl$\"3_****\\7iI_PF^cl7$$\" 3WLLL3En$4#F^cl$\"3#pmmm@Xt=%F^cl7$$\"3qmm;/RE&G#F^cl$\"3QLLL3y_qXF^cl 7$$\"3\")*****\\K]4]#F^cl$\"3i******\\1!>+&F^cl7$$\"3$******\\PAvr#F^c l$\"3()******\\Z/NaF^cl7$$\"3)******\\nHi#HF^cl$\"3'*******\\$fC&eF^cl 7$$\"3jmm\"z*ev:JF^cl$\"3ELL$ez6:B'F^cl7$$\"3?LLL347TLF^cl$\"3Smmm;=C# o'F^cl7$$\"3,LLLLY.KNF^cl$\"3-mmmm#pS1(F^cl7$$\"3w***\\7o7Tv$F^cl$\"3] ****\\i`A3vF^cl7$$\"3'GLLLQ*o]RF^cl$\"3slmmm(y8!zF^cl7$$\"3A++D\"=lj;% F^cl$\"3V++]i.tK$)F^cl7$$\"31++vV&RY2aF^cl$\"3-,+]ih2&=*F^cl7$$\"39m m;zXu9cF^cl$\"3snmmT3^q()F^cl7$$\"3l******\\y))GeF^cl$\"3q++++VAU$)F^c 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0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Cur ve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 1 8" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" " Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curv e 31" "Curve 32" "Curve 33" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 137 "N otice that the cobweb plots are similar. This is because the conjugac y takes points to points with exactly the same dynamical behavior." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "14" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }