{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {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 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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "with(LinearAlgebra):\nwith(DEtools) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dM:=M*(1-M-n*N):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dN:=N*(1-N-m*M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "Jacob:= Matrix(2,2,[[diff(dM,M),dif f(dM,N)],[diff(dN,M),diff(dN,N)]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%&JacobG-%'RTABLEG6%\"*kjGO\"-%'MATRIXG6#7$7$,(\"\"\"F/*&\"\"#F/%\"M GF/!\"\"*&%\"nGF/%\"NGF/F3,$*&F2F/F5F/F37$,$*&F6F/%\"mGF/F3,(F/F/*&F1F /F6F/F3*&F " 0 "" {MPLTEXT 1 0 29 "A:=subs(\{M = 0,N = 0\},Jacob);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTABLEG6%\"*K='\\8-%'MATRIXG6#7$7$\"\"\"\"\"!7$F/F.%'Matri xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "p:=Trace(A);\nq:=Dete rminant(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Eigenvectors(simplify(A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6%\"*gxCP\"-%'MATRIXG6#7$7#\"\"\"F+&%'VectorG 6#%'columnG-F$6%\"*!)4DP\"-F(6#7$7$\"\"!F,7$F,F8%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "System:=[diff(M(t),t) = M(t)*(1 - \+ M(t) - n*N(t)),diff(N(t),t)=N(t)*(1-N(t)-m*M(t))]:\nn:=1.1:\nm:=1.1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "DEplot(System,[M(t),N(t) ],t=0..150,M=0..1,N=0..1, arrows=comet,\n animatefield=true,numframes =50,dirfield=300);" }}{PARA 8 "" 1 "" {TEXT -1 59 "Error, (in DEtools/ DEplot/CheckDE) extra unknowns found: n\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 136286364 134961832 137247760 137250980 }{RTABLE M7R0 I6RTABLE_SAVE/136286364X,%)anythingG6"6"[gl!"%!!!#%"#"#,("""F(%"MG!"#*&%"nGF(%" NGF(!"",$*&F-F(%"mGF(F.,$*&F)F(F,F(F.,(F(F(F-F**&F1F(F)F(F.F& } {RTABLE M7R0 I6RTABLE_SAVE/134961832X,%)anythingG6"6"[gl!"%!!!#%"#"#"""""!F(F'F& } {RTABLE M7R0 I6RTABLE_SAVE/137247760X*%*algebraicG6"6"[gl!#%!!!"#"#"""F'F& } {RTABLE M7R0 I6RTABLE_SAVE/137250980X,%*algebraicG6"6"[gl!"%!!!#%"#"#""!"""F(F'F& }