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# Untitled

a guest Apr 23rd, 2019 71 Never
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1. function phaseport
2.
3. tmax=50;
4. %tip sedlo
5. %A=[1,2;4,3]; b=[1;-1]
6. %vuzel, ustoichiv zashtoto v D ima edna + sobstvena stoinost; inache
7. %razbirame tova ot dopiratelnite vektori
8. %A=[-1,0;0,-2]; b=[-1;-6]
9. %neustoichiv vuzel
10. %A=[3,1;4,3]; b=[-3;-4]
11. %fokus - ustoichiv
12. %A=[-5,1;-18,1]; b=[0;0]
13. %centur-neustoichiv
14. %A=[-2,-4;2,2]; b=[0;-2]
15. %dikritichen vuzel - neustoichiv - 2 polojiteni sobstveni stoinosti
16. A=[2,0;0,2]; b=[0;-2]
17.
18. s=A\(-b);
19. plot(s(1),s(2),'*')
20. axis([s(1)-5,s(1)+5,s(2)-5,s(2)+5])
21. hold on
22. grid on
23.
24. [T,D]=eig(A)
25.
26. % chertaem 2 pravi:
27. if imag(D(1,1)==0)
28.     xx=-10:1:10
29.     for j=1:2
30.         if T(1,1)~=0
31.             plot(xx+s(1),T(2,j)/T(1,j)*xx+s(2),'k')
32.         else
33.             plot(0*xx+s(1),xx,'k')
34.         end
35.     end
36. end
37.
38. x=s(1)-4:2:s(1)+4;
39. y=s(1)-4:2:s(1)+4;
40.
41. %mrezha:
42. [X,Y]=meshgrid(x,y)
44. for i=1:length(x)
45.     for j=1:length(y)
46.         [T,Z]=ode45(@f,[0,tmax],[X(i,j),Y(i,j)]);
47.         [T1,Z1]=ode45(@f,[0,-tmax],[X(i,j),Y(i,j)]);
48.         plot(Z(:,1),Z(:,2),Z1(:,1),Z1(:,2),'b')
49.     end
50. end
51.
52. %dyasnata strana
53. function z=f(t,y)
54. z=A*y+b;
55. end
56.
57.
58. DX=A(1,1)*X+A(1,2)*Y+b(1);
59. DY=A(2,1)*X+A(2,2)*Y+b(2);
60.
61. %normirame vektora (DX;DY) - kato go delim na duljinata mu
62. d=sqrt(DX.^2+DY.^2)
63. quiver(X,Y,DX,DY,'r')
64.
65.
66. end
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