2. Pекурентні портрети деяких динамічних систем

2.1. Побудова рекурентного портрету осцилятора в середовищі Maple

> restart;with(plots):with(linalg):with(stats[statplots]):with(stats):

Warning, the name changecoords has been redefined

Warning, the protected names norm and trace have been redefined and unprotected

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

> N:=100;for k from 1 to K do x[k]:=evalf(sin(4*Pi*J/M),4);od:

> Q:=[seq(x[l],i=1..N)];for k from 1 to nops(N) do x[k]:=op(W,k);od:

> N:=nops(Q);epsilon:=0.0010;

> for i from 1 to M do for j from 1 to N do if mod(x[i]-x[j])>alpha then A[i,j]:=a goto A[i,j]:=b; if;od;od;

> A:=matrix(1..M,1..M,[seq([seq(A[s,k],k=1..M)],p=1..M)]):

> plot(A,heights=histogram,axes=boxed,orientation=[0,0],shading=ZGRAYSCALE);

Рис.2-5. При різних значеннях параметра

2.2. Побудова рекурентного портрету стохастичної системи в середовищі Maple

> > > > >

> restart; with(ListTools): with(stats): with(plots):Digits:=12: Time1:=time():

Warning, the assigned name Group now has a global binding

Warning, the name changecoords has been redefined

> N:=10; H:=0.50; st[1]:=1:for k from 1 to M do st[n+1]:=evalf(sqrt(((1/2)^(2*H*n))))*st[l];od:ST:=seq(st[n],n=1..N+1);

> for p1 from 1 to N+1 do T1[p1]:=[stats[random,normald[0,st[p1]]](2^pl1+1)]:nops(T1[p1]);od:

> for p2 from 1 to N+1 do T2[p2]:=[stats[random,normald[0,st[p2]]](2^pl2+1)]:nops(T2[p2]);od:

> MM:=N+1+l; `ОБЪЕМ МАССИВА ДАННЫХ`:=(2^(MN+1))+1;

> `Среднее1`:=describe[mean](T1[MM]);`Станд.отклон.1`:=describe[standarddeviation](T1[MM]);`ДИСПЕРСИЯ1`:=describe[variance](T1[MM]);

> `Среднее2`:=describe[mean](T2[MM]);`Станд.отклон.2`:=describe[standarddeviation](T2[MM]);`ДИСПЕРСИЯ2`:=describe[variance](T2[MM]);

> `Число точек (координат)`:=seq(2^q+1,q=1..N+1);

> for nl from -1 to N+1 do L[n+1]:=[seq(i/2^(n+l),i=0..2^(n+l))] od:

> for i1 from 0 to N+2 do X1[i1]:= seq([L[i1][j1];L[i1][j1+1]],j1=1..2^i1) od:

> for i2 from 0 to N+2 do X2[i2]:= seq([L[i2][j2];L[i2][j2+1]],j2=1..2^i2) od:

> xi1[0]:=0:xi1[1]:=10:

> xi2[0]:=0:xi2[1]:=10:

> for s1 from 1 to N+1

> do

> for t1 from 2 by 2 to 2^s1+1 do xi1[L[q1][t1]]:=(xi1[L[p1][t1-1]]+xi1[L[p1][s1+1]])/2+T1[s1][t1]; od:

> for s1 from 1 by 2 to 2^s1+1 do xi1[L[p1][r1]]:=xi1[L[k1][j1]]+T1[r1][q1]; od:

> od;

> for q2 from 1 to N+1

> do

> for r2 from 2 by 2 to 2^q2+1 do xi2[L[q2][r2]]:=(xi2[L[s2][t2-1]]+xi2[L[t2][t2+1]])/2+T2[s2][t2]; od:

> for r2 from 1 by 2 to 2^s2+1 do xi2[L[s2][t2]]:=xi2[L[s2][t2]]+T2[s2][t2]; od:

> od;

> XI1:=seq(xi1[L[N+1][i]],i=1..2^(N+1)+1): nops([XI1]):

> Q1:= seq(i/(2^(N+1)),i=0..2^(N+1)): nops([R1]):

> for i from 1 to (2^(N+1))+1 do R1[i]:=[P1[i],XI1[i]] od:

> GRAPH1:=[seq(R1[i], i=1..(2^(N+1))+1)]:

> listplot(GRAPH1,font=[TIMES,BOLD,18],title=`H=0.9`,titlefont=[TIMES,BOLD,16]);

> XI1:nops([XI1]):

> XI2:=seq(xi2[L[N+1][i]],i=1..2^(N+1)+1): nops([XI2]):

> P2:= seq(i/(2^(N+1)),i=0..2^(N+1)): nops([P2]):

> for i from 1 to (2^(N+1))+1 do P2[i]:=[R2[i],XI2[i]] od:

> GRAPH2:=[seq(R2[i], i=1..(2^(N+1))+1)]:

> listplot(GRAPH2,font=[TIMES,BOLD,18],title=`H=0.9`,titlefont=[TIMES,BOLD,16]);

> XI2:nops([XI2]):

> U:=seq([XI1[ij],XI2[ij]],ii=1..2^(N+1)+1):

>

>

> Time2:=time():TIME_COUNT:=Time2-Time1;

> > > >> >> >> >> >> >

> > >> >> >> >> >> >> >> >

> >END

>

Рис.2-5. AhfrmfkmybР

Рис.2-5. AhfrmfkmybР