Funktion g(x), Evolutionär stabile Strategien und Replikatordynamik

>    dgl2:=diff(x(t),t)=collect(simplify(expand(x(t)*((D_A[1,1]-D_A[2,1])*(x(t)-(x(t))^2)+(D_A[2,2]-D_A[1,2])*(2*x(t)-1-(x(t))^2)))),{x(t),x(t)^2,x(t)^3});

dgl2 := diff(x(t),t) = -5*x(t)^2+3*x(t)^3+2*x(t)

>    g(x)=rhs(subs({x(t)=x},dgl2));

g(x) = -5*x^2+3*x^3+2*x

>    plot(rhs(subs({x(t)=x},dgl2)),x=0..1,labels=["x","g(x)"],axesfont=[HELVETICA,15],font=[HELVETICA,15],thickness=2);

[Maple Plot]

>    tanf:=0:
tend:=6:

>    P_max:=1:
for x_0 from 0 by 0.05 to 0.99 do
Loes:=dsolve({subs({},dgl2),x(0)=x_0},x(t),type=numeric,output=listprocedure);
P_pris[P_max]:=odeplot(Loes,[t,x(t)],tanf..tend,color=COLOR(RGB, x_0*0.8-0.1, x_0*0.8-0.1, x_0*0.8-0.1),view=[tanf..tend,0..1]):
P_pris_out[P_max]:=odeplot(Loes,[t,x(t)],tanf..tend,color=COLOR(RGB, x_0*0.8-0.1, x_0*0.8-0.1, x_0*0.8-0.1),thickness=5,view=[tanf..tend,0..1]):                                     
P_max:=P_max+1:
end do:

>    Loes11:=dsolve({subs({hsp=set_hsp,destab=set_destab,lsp=set_lsp},dgl2),x(0)=0.05},x(t),type=numeric):

>    rhs(Loes11(10)[2]):

>    Bild_ani:=display(seq(P_pris[j],j=1..P_max-1),labels=["t","x(t)"],labelfont=[HELVETICA,15],axesfont=[HELVETICA,15],font=[HELVETICA,15],thickness=2):
display(Bild_ani);

[Maple Plot]

>   

>   

>    #0.05
x_ani_01:=0.1:
x_ani_02:=0.6:
x_ani_03:=0.9:
dim_ball:=0.013:

>    #0.04
x_ani_01:=0.2:
x_ani_02:=0.6:
x_ani_03:=0.8:
dim_ball:=0.013:

>    Loes_ani1:=dsolve({subs({hsp=set_hsp,destab=set_destab,lsp=set_lsp},dgl2),x(0)=x_ani_01},x(t),type=numeric):
Loes_ani2:=dsolve({subs({hsp=set_hsp,destab=set_destab,lsp=set_lsp},dgl2),x(0)=x_ani_02},x(t),type=numeric):
Loes_ani3:=dsolve({subs({hsp=set_hsp,destab=set_destab,lsp=set_lsp},dgl2),x(0)=x_ani_03},x(t),type=numeric):
frames:=30:
for i from 0 by 1 to frames do
P_ani1[i]:=display(ellipse([i*tend/frames,rhs(Loes_ani1(i*tend/frames)[2])],tend*dim_ball,dim_ball,filled=true,color=red)):
P_ani2[i]:=display(ellipse([i*tend/frames,rhs(Loes_ani2(i*tend/frames)[2])],tend*dim_ball,dim_ball,filled=true,color=green)):
P_ani3[i]:=display(ellipse([i*tend/frames,rhs(Loes_ani3(i*tend/frames)[2])],tend*dim_ball,dim_ball,filled=true,color=blue)):
Ani[i]:=display({Bild_ani,P_ani1[i],P_ani2[i],P_ani3[i]},labels=["t","x(t)"],axesfont=[HELVETICA,15],font=[HELVETICA,15],thickness=2);
od:

>   

>    display([seq(Ani[i],i=0..frames)],insequence=true,scaling=unconstrained);

[Maple Plot]

>   

>