{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 32 "This is all the Maple syntax in \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 31 "Chapt er 8, Sections 8.5 and 8.6" }}{PARA 4 "" 0 "" {TEXT -1 75 "An Introduc tion to the Mathematics of Biology, with Computer Algebra Models" }} {PARA 4 "" 0 "" {TEXT -1 34 "by Yeargers, Shonkwiler, & Herod. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "The Synta x is written for Maple 6" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Page 257" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "Ena:=55: Ek:=-82: El:= -59: gkbar:= 24.34: gnabar:=70.7: \ngl:=0.3: vrest:=-69: cm:=0.001:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 269 "alphan:=v-> 0.01*(10-(v-vrest))/(e xp(0.1*(10-(v-vrest)))-1):\nbetan:=v-> 0.125*exp(-(v-vrest)/80):\nalph am:=v-> 0.1*(25-(v-vrest))/(exp(0.1*(25-(v-vrest)))-1):\nbetam:=v-> 4* exp(-(v-vrest)/18):\nalphah:=v->0.07*exp(-0.05*(v-vrest)):\nbetah:=v-> 1/(exp(0.1*(30-(v-vrest)))+1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "pulse:=t->-20*(Heaviside(t-.001)-Heaviside(t-.002)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 264 "rhsV:=(t,V,n,m,h)->-(gnabar *m^3*h*(V-Ena) +\n\011\011\011\011\011\011gkbar*n^4*(V-Ek) + gl*(V-El) + pulse(t))/cm:\nrhsn:=(t,V,n,m,h)-> 1000*(alphan(V)*(1-n) - betan(V)* n):\nrhsm:=(t,V,n,m,h)-> 1000*(alpham(V)*(1-m) - betam(V)*m):\nrhsh:=( t,V,n,m,h)-> 1000*(alphah(V)*(1-h) - betah(V)*h):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 52 "inits:=V(0)=vrest,n(0)=0.315,m(0)=0.042, h(0 )=0.608;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 270 "sol:=dsolve(\{ diff(V(t),t)=rhsV(t,V(t),n(t),m(t),h(t)),\n diff(n(t),t)=rhsn(t,V (t),n(t),m(t),h(t)),\n diff(m(t),t)=rhsm(t,V(t),n(t),m(t),h(t)), \n diff(h(t),t)=rhsh(t,V(t),n(t),m(t),h(t)),inits\},\n \{V(t ),n(t),m(t),h(t)\},type=numeric, output=listprocedure);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Vs:=subs(sol,V(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(Vs,0..0.02);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 12 "Figure 8.6.2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a:=0.7; b:=0.8; c:=0.08;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "rhsx:=(t,x,y)->x-x^3/3-y;\nrhsy:=(t,x,y)->c*(x+a-b* y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "sol2:=dsolve(\{diff (x(t),t)=rhsx(t,x(t),y(t)),\n diff(y(t),t)=rhsy(t,x(t),y( t)),x(0)=0,y(0)=-1\},\n \{x(t),y(t)\},type=numeric, output=listpr ocedure);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "xs:=subs(sol2, x(t)); ys:=subs(sol2,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "K:=plot([xs,ys,0..200],x=-3..3,y=-2..2):\nJ:=plot(\{[V,(V+a)/b,V= -2.5..1.5],[V,V-V^3/3,V=-2.5..2.2]\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plots[display](\{J,K\});" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "2 0" 31 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }