Need the backward trajectories of ode plot

Question

Atom 2013-7-14

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https://ww2.mathworks.cn/matlabcentral/answers/82016-need-the-backward-trajectories-of-ode-plot

I have a system of differential equations which I can solve by Euler's method. The following code gives a plot of a trajectory that starts from x(1)=0.7; y(1)=0.11; and depicts its evolution in forwarding time. But I need a trajectory that starts from x(1)=0.7; y(1)=0.11; and evolved in backward time. That mean what will be the plot if t tends to -infinity. Please correct my code so that I can get backword evolution of trajectories:

clear
alpha=.5;gamma=1; delta=0.3; L=.4; beta=1.778; 
x(1)=0.7;
y(1)=0.11;
t(1)=0;
for i=1:50000
    t(i+1)=t(i)+.01;
    x(i+1)=x(i)+.01*[x(i)*((1-x(i))*(x(i)/L-1)-beta*y(i)/(x(i)+alpha))];
    y(i+1)=y(i)+.01*[beta*x(i)*y(i)/(x(i)+alpha)-gamma*y(i)-delta*y(i)^2];
end
plot(x,y, 'b')
axis([.4 1 0 .22])

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Answer 1

Jan 2013-7-14

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https://ww2.mathworks.cn/matlabcentral/answers/82016-need-the-backward-trajectories-of-ode-plot#answer_91744

在 MATLAB Online 中打开

Do you ask for changing the line:

t(i+1) = t(i) + 0.01;

to

t(i+1) = t(i) - 0.01;

?

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Atom 2013-7-16

编辑：Atom 2013-7-16

在 MATLAB Online 中打开

Do you mean this?

alpha=.5;gamma=1; delta=0.3; L=.4; beta=1.778; 
  x(50000)=0.7;
  y(50000)=0.11;
  t(50000)=0;
  for i=50000:1
      t(i+1)=t(i)-.01;
      x(i+1)=x(i)+.01*[x(i)*((1-x(i))*(x(i)/L-1)-beta*y(i)/(x(i)+alpha))];
      y(i+1)=y(i)+.01*[beta*x(i)*y(i)/(x(i)+alpha)-gamma*y(i)-delta*y(i)^2];
  end
  plot(x,y, 'b')
  axis([.4 1 0 .22])

But this does not servers the purpose. Please help me to solve the issue. I am very sorry for the inconvenience for the repeated request.

Jan 2013-7-16

编辑：Jan 2013-7-16

在 MATLAB Online 中打开

"for i=50000:1" does not enter the loop at all. You need the stepsize of -1.

I cannot test it currently, but let me guess:

for i = 50000:-1:2
  t(i-1) = t(i) - 0.01;
  x(i-1) = x(i) + 0.01*[x(i)*((1-x(i))*(x(i)/L-1)-beta*y(i)/(x(i)+alp ha))];
  y(i-1) = y(i) + 0.01*[beta*x(i)*y(i)/(x(i)+alpha)-gamma*y(i)-delta*y(i)^2];
end

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