???????????? ?? ????????, ??? ??????? ???? ????, ?

????????????????????? ??????????? ???????«?????????????????????? ???????? ?????????? ???????????»??????????????????? ????????????????? ?????????? ??????????   ??????????? ?????? ?1? ?????????? «?????????? ??????»??????????? ??????? ?????? ?????????? ????????????? 14       ???????: ?????????: ??????? ????? ??-41 ????? ?.?. ?????? ?. ?.

              ???? —2017   ?????     ??????.. 3 ??????? ???????.. 5 1 ??????????? ????’???? ??????? ??????????????? ???????. 5 2 ??????????? ??????? ?????????? ??????? ?? ????????? MATLAB.. 8 ??????? ?.

. 14    ?????? ????? ? ????????? ????????? ?????????????????????? ???????                                                                         (1) ?? , x = x(t), y = y(t)— ??????????, t— ?????? ????.??? ???????? ??????? ?????? (??????????) ????? ???????????? ??????????????????????? ?????????:                                                         (2)??  — ????? ????????, N — ?????????????????,  — ???????? ????? (??? ????????? ?????????????? ??????? ????????? (2)),  — ?????????? ?????? ????????? ?????? ? ?????  (?????, , , ?? , ), ,  – ????????? ?????? ?? ????????? ????? x ??y . ????????? ???????? ???????? ???? ????? ? ???? ?? ?????????? ??? ???????? ?????????? (????? ? ????????? ” (k – 1) -?? ?????????”????????????? ? ???????? ” k -?? ?????????” ?????? ???????,???? ????????? ???????? ????????? ? ???????? ?????). ?????, ??? ??????????????????? ?????????? ???????, ?? ???????? ? ????? , ????? ??? ????????? ??????????(?????,  ?? ) ???? ?’?????? ????????? ??????.??? ?????, ???????? ????? ????????? (; (??? ???????? ? ?? ????????, ?????????? ???? ????, ? ??? ?????? ???? ???????? ??????????? ??????????). ???????? ????????? ?????????? ????????????????? ??????????????? ??????? (???? ?????????, ???????????? ?????????,???????????) ????? ??????????, ?? ????’?????? ???????, ?? ?????? ?????????????? ??????? ??????? ????? (?????????????? ??????? ???????).

?????  – ?????? ??????? ?????, ????? ????????????????? ???????? (1). , ???? ??????? ?????????????? ??????? ?? ?????????, ????? , ?? ????????????? ???????? ??????? (??????? (*)): ??? ??????? ????? ??????????? ??????? ??????? ??????? ??? ????????? ????? ????? ????? ????? ?????????? ? ???’????? ??????? ???????? ??????? ????? ?????????? ? ????????? ??????? ???????? ????????? ????? ?????? ???’???? ??????? ????? ?????? ??????? ????????? ????? ?????? ?????? ?????? ?????  ??????? ???????1??????????? ????’???? ??????? ?????????????????????? ????????? ?????????????? ?????????? ??????? (1.1) ?????? ???????? 14:                                          (1.1)???????????????? ??????? ???? ??????? ??????? (1.1) ?? ???? ???????? ???????? (???????????) ????? ???????: ?(4; 1), ?(2; 2),C(-2; -2).??????? ?????(???????? ????????) ?????????????? ??????? ??? ??????: J =                                           (1.2) J(?) = J(4, 1) =                                       (1.

Best services for writing your paper according to Trustpilot

Premium Partner
From $18.00 per page
4,8 / 5
4,80
Writers Experience
4,80
Delivery
4,90
Support
4,70
Price
Recommended Service
From $13.90 per page
4,6 / 5
4,70
Writers Experience
4,70
Delivery
4,60
Support
4,60
Price
From $20.00 per page
4,5 / 5
4,80
Writers Experience
4,50
Delivery
4,40
Support
4,10
Price
* All Partners were chosen among 50+ writing services by our Customer Satisfaction Team

3)?????? ???????????? (1.3): ?1,2 = -1±. ????????????????????? (*), ????????, ?? ?. A – ??????? ?????.????????? ???????? ???????????? ???????? ?? ????????? ??????? ?????????:  ???? ??? ??????????? ?? ???????????? ????????. J(B) = J(2, 2) =                                         (1.

4) ?????? ???????????? (1.4): ?1,2 =±.????????????????????? (*), ????????, ?? ?. B – ?????.?????? ?????????????? (1.4): S1 = (-, 1); S2 = (); J(?) = J(-2, 2) =                                     (1.5)?????? ???????????? (1.

4): ?1,2 = -4±.????????????????????? (*), ????????, ?? ?. C – ??????? ?????.????????? ???????? ???????????? ???????? ?? ????????? ??????? ?????????:  ???? ??? ??????????? ????? ???????????? ???????.  ??????? 1.1 – ??????? ??????? ??????? Wolfram (1.1) ??????? 1.

2 – ????? ????????? ??????? ?????????????? Graph Phase Plane (1.1) 2??????????? ??????? ?????????? ??????? ??????????? MATLAB  ????????? ?????? ?????, ?????????????? ?? ?’?????? ????????? ??????? ?????? ? ?????? ????? ???????????????????? ?????????? ????????? ???????(2).?? ??????? 2.

1. ????????? ?????? ????? ? ???????????????? (4;2). ?????? ????? ?????????? ?? ????????? ?????  ???  =  =0,01.

  ???????2.1 – ????? ????? ? ?????????? ?????? (4;2) ???????? ????????? ????? (0;0)??? ??? ?? ??????. ????????? ?? ??????? 2.2. ???????2.2 – ????? ????? ? ?????????? ?????? (0;0) ???????? ????????? ??????  ?  ???????? ??? ???????? ???????? ???????? ? ??????????? ?? ?? 10-2,????????? ????? ?????? ???????? . ????????????????? ?????? ???? ?????? ????? (3;3).

??????? ??????? ??????????? ???. 2.3. ??????? 2.3 – ??????? ??????? ??? ??????  ? ??? ??? ?????????? ????????  ?  = 10-1 . ????????? ????? ???????? ?????????? ??????????? ? ????? ???????????? ????? (2;2), ???.

??????? 2.4. ??????? 2.4 – ??????? ??????? ??? ????????  ? ????? ??????? ????????? ????????: N=100 ?? ?????????  ?  = 10-3.?????????? ????????? ?? ??????? 2.5 ? ???????? ??????????? ?? ????????????? ????????? ???????.????? 2.5 – ??????? ??????? ??? ????????  ?  ?? N ?? ??????? 2.

6 ?? 2.7 ?? ????????? ???????????????? ?????? ? ????? ????????? ????? ????? ?(4;1). ??????? 2.

6 – ????????? ??????? ?????? ? ?????????? ?(4;1).??????? 2.7 – ????????? ??????? ?????? ? ??????????(????????? ???????) ?(4;1). ?? ??????? 2.8 ????????? ????????? ??????? ?????? ? ?????????? ?(2;2).  ??????? 2.

8 – ????????? ??????? ?????? ? ?????????? ?(2;2).?? ??????? 2.9 ????????? ????????? ????????????? ? ????? ????? ?(-2;-2).??????? 2.9 – ????????? ??????? ?????? ? ????? ????? ?(-2;-2).???????? ??????????? ????????????????????? ?????? ? ??????????? ????’???? ???????,??????????? ???????????: ?(4; 1), ?(2; 2), C(-2; -2), ?????????? ?? ???? (??? ?????? ?????? ?? ?????).

???????  ??????? ???? ?????????? ?? ????????? Wolfram ?? Graph Phase Plane.????? ?????????? ???????? ??? ???????? ????????????? ? ??????? ?????, ???????? ???????? ??????? ??? ?????? ?????????? ????? (????? ???? ??????????? ????????? ???????? ?????) ?? ??? ????????? ????????? ??????? ? ????? ????? ??????.  ??????? ? Listingmathanalys.ma=1;while a>0    disp(‘1.

Build the pathfrom the given point’)    disp(‘2. Build phaseportrait ‘)    disp(‘3. Show the systembehaviour around peculiar points’)    a=input(‘Chose your number: ‘);    if a==1         x0=input(‘Input starting point for x: ‘);         y0=input(‘Input starting point for y: ‘);         N=input(‘Inputa number of points ‘);         parametr1 =input(‘Input parametr for x ‘);         parametr2 =input(‘Input parametr for y ‘);         x,y =phase(x0,y0,N,parametr1,parametr2);         figure          plot(x,y)    elseif a==2         x0=input(‘Input starting point for x: ‘);         y0=input(‘Input starting point for y: ‘);         N=input(‘Inputa number of points ‘);         Nx=input(‘Input a number of points for x: ‘);         Ny=input(‘Input a number of points for y: ‘);         dx=input(‘Input a step between starting points for x: ‘);         dy=input(‘Input a step between starting points for y: ‘);         parametr1 =input(‘Input parametr for x ‘);         parametr2 =input(‘Input parametr for y ‘);        phase(x0,y0,N,Nx,Ny,dx,dy,parametr1,parametr2) ;      elseif a==3          x0=input(‘Input starting point for x: ‘);         y0=input(‘Input starting point for y: ‘);         N=input(‘Inputa number of points ‘);         parametr1 =input(‘Input parametr for x ‘);         parametr2 =input(‘Input parametr for y ‘);        phase(x0,y0,N,20,20,0.1,0.1,parametr1,parametr2) ;    endend    phase.m:function phase(x00,y00,N,nx,ny,dx,dy,parametr1,parametr2)  x0=x00 – (nx/2)*dx;y0=y00 – (ny/2)*dy; x,y=path(x0,y0,N,parametr1,parametr2); figureplot(x,y)  holdon p1= x0; for k=2:nx    p1 = p1 + dx;     p2 = y0;         for j=2:ny             p2 = p2 + dy;            x,y=path(p1,p2,N,parametr1,parametr2);             plot(x,y)         end endholdoff   path.m:function x,y = path(x0,y0,N,parametr1,parametr2) x =zeros(N,1); y =zeros(N,1); x(1)= x0; y(1)= y0;  for i=2:N     Vx = ((x(i-1))*(y(i-1)))-4;     Vy = (x(i-1)-4)*(y(i-1)-x(i-1));     Vvx = Vx/power(Vx*Vx+Vy*Vy,1/2);     Vvy = Vy/power(Vx*Vx+Vy*Vy,1/2);     x(i)= x(i-1) + parametr1*Vvx;     y(i)= y(i-1) + parametr2*Vvy; end