方程组的奇点问题.rar_奇点_常微分_方程的奇点_方程组的奇点_相图

clc,clear,close all

global a y0

a = -1; %取不同值观察相图

yy = {[0;0], [2/9;0], [-1;-6.2/9], [-1;-11.8/9], ...

[-1;-21/9], [-0.5;-21/9], [-0.5;-22.5/9], [1;-7.1/9], [1;-13.8/9],

[1;-21/9]};

for i = 1:5

y0 = yy{i};

solve_the_P268()

[t, y] = ode45(@odefun,[-2 2], y0);

% figure()

hold on

[X,Y] = meshgrid(y(:, 1), y(:, 2));

streamslice(X,Y,a.*X+(Y+1).*(2.*Y.*Y+4.*Y+3),-X-2*X.^3);

function dydt = odefun(t,y)

dydt = zeros(2,1);

dydt(1) = a*y(1) + (y(2)+1)*(2*y(2)*y(2)+4*y(2)+3);

dydt(2) = -y(1)-2*y(1)^3;

end

end

(a) a>2