## 15 Reputation

2 years, 144 days

## asymptotically stable...

Maple

howca i determine the range of gains if g(x)=1/(x+x^2+x^3+2)

the answer is like closed loop

## smother curve using interpolation Packag...

Maple

This is the same example in previous post,

But here my question is how to produce smother plot of date. I tried the interpolation package but it not working..

 > restart:
 > with(LinearAlgebra): with(CurveFitting): with(Interpolation): with(plots): with(Statistics): Omega:=0.1:no:=0:Delta:=0:tau0:=1:c:=0:gamma1:=0: j:=1:k1:=0:t:=1:xr:=1:Gamma:=0.1:
 > for i from -10 to 10 do d[i]:=i: b:=sum(-gamma1*tau0+I*tau0*Delta-2*a*(k-1)*xr,k=0..1): a:=1+I*c; c1:=sqrt(conjugate(a))/tau0: c2:=0.5*((conjugate(b)/sqrt(conjugate(a)))): lambda1[i]:=2*(Gamma-I*d[i])*(t-k1)/j+(Gamma-I*d[i])^2: lambda2[i]:=t*(1-j)-k1/j+1/sqrt(2)*(Gamma-I*d[i]): lambda3[i]:=c1*(t-k1)/j+c1*(Gamma-I*d[i])+c2: J1[i]:=sqrt(Pi)/sqrt(2)*(1-erf(lambda2[i])); J1mod[i]:=(Re(J1[i]))^2+(Im(J1[i]))^2:
 > g1[i]:=0.5*sqrt(Pi)*tau0*exp(c2^2)     *exp(-conjugate(a)*((k-1)*xr)^2)/(sqrt(conjugate(a)));
 > F2[i]:=map(fnormal,evalf(sqrt(2)*Int(unapply(exp(-x^2)*erf(-sqrt(2)*c1*x+lambda3[i]),x),-lambda2[i]..5,epsilon=1e-5)));
 > J2[i]:=sum(g1[i]*J1[i]+g1[i]*F2[i],k=1..1);
 > J2mod[i]:=abs(J2[i])^2: h1[i]:=map(fnormal,evalf(exp(-d[i]^2))): f[d[i]]:=map(fnormal, evalf(h1[i]*(no*J1mod[i]+Omega^2*J2mod[i]))): #f[d[i]]:=-d[i]^2*log(exp(1))+2*log(Omega)+log(J2mod[i]): #map(simplify~, %[2], zero): end do:
 > with(CurveFitting): ptsN1 := CodeTools:-Usage(            [seq([d[i], evalf(f[d[i]])], i = -10 .. 10)]                          ):
 memory used=3.44KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns, gc time=0ns
 >
 > P1:=plot(ptsN1, color = black, linestyle = solid, thickness = 2,      color = black, axes = boxed, labelfont = ["HELVETICA", 14],      labels = ["d", "S_M(d)"]);
 >
 > points := [seq(x, x = -10 .. 10, 1)]: data   := [seq(evalf(f[d[i]]), i = -10 .. 10, 1)]: f := Interpolate(points, data): plot(f,-10..10);
 >
 >

I noticed this package is not introduced in Maple 17.. what is the alternative way to produce smother curve

## limit of the integral is function...

Maple

Hi

The integration in (F2) is not work properly.

My tyr is below:

restart:with(plots):
assume(d,real):

b:=-gamma1*tau0+I*tau0*Delta-2*a*(k-1)*xr:
a:=1+I*c;
c1:=sqrt(conjugate(a))/tau0:
c2:=0.5*((conjugate(b)/sqrt(conjugate(a)))):
lambda1:=2*(1-I*d)*(t-k1)/j+(1-I*d)^2:
lambda2:=t*(1-j)*k1/j+1/sqrt(2)*(1-I*d):
lambda3:=c1*(t-k1)/j+c1*(1-I*d)+c2:
J1:=sqrt(Pi)/sqrt(2)*(1-erf(lambda2)):
J1mod:=(Re(J1))^2+(Im(J1))^2:
g1:=0.5*sqrt(Pi)*tau0*exp(c2^2)*exp(-conjugate(a)*((k-1)*xr)^2)/(sqrt(conjugate(a))):

F2:=-sqrt(2)*int(exp(-x^2)*erf(sqrt(2)*c1*x+lambda3),x=-lambda2..infty);
Warning,  computation interrupted
J2:=sum(g1*J1+g1*F2,k=1..1);
J2mod:=(((Re(J2))^2+(Im(J2))^2)):
W:= unapply(no*J1mod+Omega^2*J2mod,d):
Omega:=0.01:no:=1:Delta:=0:tau0:=1:c:=0:gamma1:=0:j:=1:k1:=0:t:=2*Pi:xr:=1:
P1:=plot(W,-50..50,axes=boxed,title=tit,color=black,font=[2,3,18],thickness=2,tickmarks=[3,2],titlefont=[SYMBOL,14],font=[1,1,18],linestyle=1);

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