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close all; clear all; TS_lab_04 function TS_lab_04 tspan1 =[0 0.25]; tspan2 =[0.251 0.50]; tspan3 =[0.501 0.75]; tspan4 =[0.751 1]; x0_1 =[1 0 0]; a1 =0.04; b1 =0.6; c1 = 0.2; a2 =0.05; b2 = 0.35; c2 =0.37; a3 = 0.13; b3 =0.0067; c3 =0.2; a4 0.1; b4 =0.4; c4 = 0.3; [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a1 , b1 , c1 ) , tspan1 , x0_1 ); x3 =1 - xsol (: ,1) - xsol (: ,2); z1 =[0.25 ,0.25]; z2 =[0.5 ,0.5]; z3 =[0.75 ,0.75]; y =[0 ,1]; figure (1); hold on ; grid on ; plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ ); title ( ’ Wykres ␣ x ( t ) ’ ); xlabel ( ’t ’ ); ylabel ( ’x ( t ) ’ ); % legend ( ’x1 ’ , ’x2 ’ , ’x3 ’); x0_2 =[ xsol (end ,1) xsol (end ,2) x3 (end )]; [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a2 , b2 , c2 ) , tspan2 , x0_2 ); x3 =1 - xsol (: ,1) - xsol (: ,2); plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ ); x0_3 =[ xsol (end ,1) xsol (end ,2) x3 (end )]; [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a3 , b3 , c3 ) , tspan3 , x0_3 ); x3 =1 - xsol (: ,1) - xsol (: ,2); plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ ); x0_4 =[ xsol (end ,1) xsol (end ,2) x3 (end )]; [ tsol , xsol ] = ode45 ( @ (t , x ) odefcn (t ,x , a4 , b4 , c4 ) , tspan4 , x0_4 ); x3 =1 - xsol (: ,1) - xsol (: ,2); plot ( tsol , xsol (: ,1) , ’r ’ , tsol , xsol (: ,2) , ’b ’ , tsol , x3 , ’g ’ ); plot ( z1 ,y , ’k - - ’ ); plot ( z2 ,y , ’k - - ’ ); plot ( z3 ,y , ’k - - ’ ); t1 =0:0.001:0.25; t2 = t1 +0.25; t3 = t2 +0.25; t4 = t3 +0.25; u1 = @ ( t ) min (max ( a1 .* t + b1 , 0) , 1); u2 = @ ( t ) min (max ( a2 .* t .* t + b2 .* t + c2 , 0) , 1); 4 u3 = @ ( t ) min (max ( a3 .* t .* t + b3 .* t + c3 , 0) , 1); u4 = @ ( t ) min (max ( a4 .* t + b4, 0) , 1); figure (2); hold on ; grid on ; title ( ’ Wykres ␣ czterech ␣ funkcji ␣ u ( t ) ␣ zmiennych ␣ na ␣ p r z e d z i a a c h ’ ); xlabel ( ’t ’ ); ylabel ( ’u ( t ) ’ ); plot ( t1 , u1 ( t1 )); plot ( t2 , u2 ( t2 )); plot ( t3 , u3 ( t3 )); plot ( t4 , u4 ( t4 )); plot ( z1 ,y , ’k - - ’ ); plot ( z2 ,y , ’k - - ’ ); plot ( z3 ,y , ’k - - ’ ); end function dxdt = odefcn (t ,x ,a ,b , c ) u = a * t * t + b * t + c ; if u >1 u =1; end if u <0 u =0; end dxdt = zeros (3 ,1); dxdt (1) = u *(10* x (2) - x (1)); dxdt (2) = u *( x (1) -10* x (2)) -(1 - u )* x (2); end
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