{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 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 "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 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 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 42 "with(linalg): with(plots): with(DE tools):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names n orm and trace have been redefined and unprotected\n" }}{PARA 7 "" 1 " " {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }} {PARA 7 "" 1 "" {TEXT -1 45 "Warning, the name adjoint has been redefi ned\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eq1:=diff(A(t),t)= r*A*(1-A/K1-alpha*B/K1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/-% %diffG6$-%\"AG6#%\"tGF,*(%\"rG\"\"\"F*F/,(F/F/*&F*F/%#K1G!\"\"F3*(%&al phaGF/%\"BGF/F2F3F3F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "eq 2:=diff(B(t),t)=r*B*(1-beta*A/K2-B/K2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/-%%diffG6$-%\"BG6#%\"tGF,*(%\"rG\"\"\"F*F/,(F/F/*(%%beta GF/%\"AGF/%#K2G!\"\"F5*&F*F/F4F5F5F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "F:=rhs(eq1);G:=rhs(eq2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG*(%\"rG\"\"\"%\"AGF',(F'F'*&F(F'%#K1G!\"\"F,*(%&a lphaGF'%\"BGF'F+F,F,F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG*(%\"r G\"\"\"%\"BGF',(F'F'*(%%betaGF'%\"AGF'%#K2G!\"\"F.*&F(F'F-F.F.F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "J:=jacobian([F,G],[A,B]);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'matrixG6#7$7$,&*&%\"rG\"\"\" ,(F-F-*&%\"AGF-%#K1G!\"\"F2*(%&alphaGF-%\"BGF-F1F2F2F-F-*(F,F-F0F-F1F2 F2,$**F,F-F0F-F4F-F1F2F27$,$**F,F-F5F-%%betaGF-%#K2GF2F2,&*&F,F-,(F-F- *(F " 0 "" {MPLTEXT 1 0 46 "equilib:=solve(\{rhs(eq1)=0,rhs(eq2)=0\},\{A, B\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(equilibG6&<$/%\"AG\"\"!/% \"BGF)<$F'/F+%#K2G<$F*/F(%#K1G<$/F+*&,&F.!\"\"*&%%betaG\"\"\"F1F9F9F9, &*&F8F9%&alphaGF9F9F9F6F6/F(*&,&F1F6*&F " 0 "" {MPLTEXT 1 0 35 "J1:=subs(op(1,[equilib]),evalm(J)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#J1G-%'matrixG6#7$7$%\"rG\"\"!7$ F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evJ1:=eigenvals(J1) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%evJ1G6$%\"rGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "J2:=subs(op(2,[equilib]),evalm(J)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#J2G-%'matrixG6#7$7$*&%\"rG\"\" \",&F,F,*(%&alphaGF,%#K2GF,%#K1G!\"\"F2F,\"\"!7$,$*&F+F,%%betaGF,F2,$F +F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evJ2:=eigenvals(J2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%evJ2G6$,$*(%\"rG\"\"\",&%#K1G! 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