DYNAMICZNE SPR6

ZAD 2 VAN DER POL
% Paweł Pytlowski

% czyszczenie workspace'u i otwartych wykresów
clc;
close all;
clear;

% deklarowanie globalności zmiennej epsilon dla ułatwienia
global eps;

% ustawianie parametrów do symulacji
dt = 0.05;
T = [0 5];
wpc=[linspace(-5,5,50);linspace(-5,5,50)];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

eps=-0.01;

figure;
hold on;
for i=1:length(wpc)
    X=solver(@vanderpol, [wpc(1,i) ;wpc(2,i) ] ,T,dt);
    plot(X(1,:),X(2,:));
end
title(strcat('Epsilon=', num2str(eps)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

eps=0;

figure;
hold on;
for i=1:length(wpc)
    X=solver(@vanderpol, [wpc(1,i) ;wpc(2,i) ] ,T,dt);
    plot(X(1,:),X(2,:));
end
title(strcat('Epsilon=', num2str(eps)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

eps=0.1;

figure;
hold on;
for i=1:length(wpc)
    X=solver(@vanderpol, [wpc(1,i) ;wpc(2,i) ] ,T,dt);
    plot(X(1,:),X(2,:));
end
title(strcat('Epsilon=', num2str(eps)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

eps=1;

figure;
hold on;
for i=1:length(wpc)
    X=solver(@vanderpol, [wpc(1,i) ;wpc(2,i) ] ,T,dt);
    plot(X(1,:),X(2,:));
end
title(strcat('Epsilon=', num2str(eps)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

eps=1.55;

figure;
hold on;
for i=1:length(wpc)
    X=solver(@vanderpol, [wpc(1,i) ;wpc(2,i) ] ,T,dt);
    plot(X(1,:),X(2,:));
end
title(strcat('Epsilon=', num2str(eps)));
hold off;





























ZAD 3

% Paweł Pytlowski

% czyszczenie workspace'u i otwartych wykresów
clc;
close all;
clear;

% deklarowanie globalności zmiennej a dla ułatwienia
global a;

% ustawianie parametrów do symulacji
T = [0 2];
dt = 0.005;
wpc=[-3:0.1:3];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja
a = -0.5;
figure;
hold on;
for i=1:length(wpc)
    X=solver(@system3, wpc(i),T,dt);
    plot(T(1):dt:T(2),X);
end
title(strcat('a=', num2str(a)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

a = 0;
figure;
hold on;
for i=1:length(wpc)
    X=solver(@system3, wpc(i),T,dt);
    plot(T(1):dt:T(2),X);
end
title(strcat('a=', num2str(a)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

a = 1;
figure;
hold on;
for i=1:length(wpc)
    X=solver(@system3, wpc(i),T,dt);
    plot(T(1):dt:T(2),X);
end
title(strcat('a=', num2str(a)));
hold off;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ustawienie parametru a i symulacja

a = 4;
figure;
hold on;
for i=1:length(wpc)
    X=solver(@system3, wpc(i),T,dt);
    plot(T(1):dt:T(2),X);
end
title(strcat('a=', num2str(a)));
hold off;













ZAD 4 LORENZ

% Paweł Pytlowski

% czyszczenie workspace'u i otwartych wykresów
clc;
close all;
clear;

% deklarowanie globalności zmiennych dla ułatwienia
global sigma;
global r;
global b;

% ustawianie parametrów do symulacji
wpc=[linspace(-5,5,20);linspace(-5,5,20);linspace(-5,5,20);];
T = [0 5];
dt = 0.01;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% wartości z konspektu
sigma=10;
r=28;
b=8/3;

% symulacja portretu w R3
figure;
grid on;
hold on;
for i=1:length(wpc)
    X=solver(@lorenz, [wpc(1,i) ; wpc(2,i) ; wpc(3,i)],T,dt);
    plot3(X(1,:),X(2,:),X(3,:));
end
hold off
view(20, 10);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% trajektoria typu "oczy kosmity"
sigma=40;
r=30;
b=11;

% symulacja portretu w R3
figure;
grid on;
hold on
for i=1:length(wpc)
    X=solver(@lorenz, [wpc(1,i) ; wpc(2,i) ; wpc(3,i)],T,dt);
    plot3(X(1,:),X(2,:),X(3,:));
end
hold off
view(20, 10);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% trajektoria typu "maska karnawałowa"
sigma=52;
r=44;
b=11;

% symulacja portretu w R3
figure;
grid on;
hold on
for i=1:length(wpc)
    X=solver(@lorenz, [wpc(1,i) ; wpc(2,i) ; wpc(3,i)],T,dt);
    plot3(X(1,:),X(2,:),X(3,:));
end
hold off
view(20, 10);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

sigma=0; % wartości zerowe
r=0;
b=0;

% symulacja portretu w R3
figure;
grid on;
hold on
for i=1:length(wpc)
    X=solver(@lorenz, [wpc(1,i) ; wpc(2,i) ; wpc(3,i)],T,dt);
    plot3(X(1,:),X(2,:),X(3,:));
end
hold off
view(20, 10);