{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 } {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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 82 " Consider the competing species P and Q that satisfies the differential equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "dP/dt = R*P(t )*(1-P(t)/K)-s*P(t)*Q(t);" "6#/*&%#dPG\"\"\"%#dtG!\"\",&*(%\"RGF&-%\"P G6#%\"tGF&,&F&F&*&-F-6#F/F&%\"KGF(F(F&F&*(%\"sGF&-F-6#F/F&-%\"QG6#F/F& F(" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "dQ/dt = -u*Q(t)+v*P(t)*Q(t);" "6#/*& %#dQG\"\"\"%#dtG!\"\",&*&%\"uGF&-%\"QG6#%\"tGF&F(*(%\"vGF&-%\"PG6#F/F& -F-6#F/F&F&" }{TEXT -1 0 "" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "dsolve(\{diff(P(t),t)=R*P(t)-R/K*P(t)-S* P(t)*Q(t),diff(Q(t),t)=-U*Q(t)+V*P(t)*Q(t),P(0)=N,Q(0)=M\},\{P(t),Q(t) \}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "R := 0.2; K := 100; S := 0.005; U := 0.01; \+ V := 0.015;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "N := 25; M : = 15;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "dsolve(\{diff(P(t),t)=R*P(t)-R/K*P(t)-S* P(t)*Q(t),diff(Q(t),t)=-U*Q(t)+V*P(t)*Q(t),P(0)=N,Q(0)=M\},\{P(t),Q(t) \});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "p := dsolve(\{diff (P(t),t)=R*P(t)-R/K*P(t)-S*P(t)*Q(t),diff(Q(t),t)=-U*Q(t)+V*P(t)*Q(t), P(0)=N,Q(0)=M\},\{P(t),Q(t)\},type=numeric,method=taylorseries);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "odeplot(p, [P(t),Q(t)],t=0..8);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "R := 0.07; K := 100; S := 0.025; U := 0.95; V := 0.05;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "N := 25; M := 15;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "U/V; R/S*(1-U/(K*V));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "p := dsolve(\{diff( P(t),t)=R*P(t)-R/K*P(t)-S*P(t)*Q(t),diff(Q(t),t)=-U*Q(t)+V*P(t)*Q(t),P (0)=N,Q(0)=M\},\{P(t),Q(t)\},type=numeric,method=taylorseries);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "odeplot(p, [P(t),Q(t)],t=0..40);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "odeplot(p, [t,P(t)],t=0..40);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "odeplot(p, [t,Q(t)],t=0..40);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }