How to solve a system of differential equations without symbolic math lab

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Anna 2019-11-8

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评论： Walter Roberson 2019-11-8

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I have three equations that are similar to these,

a, b, c, d, and e are all known and I have initial conditions for X, Y, and Z. I have equations saved in their own functions like this:

function dX = fun_dX(a,b,c,d,X,Y)
dX = a*X*(1-b*X)-c*X*Y-d
end

What functions/code should I be using to solve the system without the use of symbolic math lab? Also, how do I get it in a form that I can plot my answers all on one graph (using hold on)? I tried ode45 to solve them individually (for example solving the first equation with a given Y) but I believe the use of ode45 was wrong because the graph of X vs. t did not make sense.

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Walter Roberson 2019-11-8

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https://ww2.mathworks.cn/matlabcentral/answers/489878-how-to-solve-a-system-of-differential-equations-without-symbolic-math-lab#answer_400443

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a = whatever; b = whatever; c = whatever; d = whatever; e = whatever;
[t, xyz] = ode45(@(t, XYZ) odefun(t, XYZ, a, b, c, d, e), tspan, xyz0);
plot(t, xyz);
function dXYZ = odefun(t, XYZ, a, b, c, d, e)
   X = XYZ(1); Y = XYZ(2); Z = XYZ(3);
   dXYZ(1) = a*X*(1-b*X) - c*X*Y - d;
   dXYZ(2) = a + b*Y - d*X.^2*Y - c*X*Y;
   dXYZ(3) = e*Z + b^2*Z - c*Z*X _ d*Y*Z;
end

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Anna 2019-11-8

What do you mean by that? I've tried changing xyz0 but it hasn't gotten rid of the errors.

Walter Roberson 2019-11-8

在 MATLAB Online 中打开

function dXYZ = odefun(t, XYZ, a, b, c, d, e)
   X = XYZ(1); Y = XYZ(2); Z = XYZ(3);
   dXYZ(1,1) = a.*X.*(1-b.*X) - c.*X.*Y - d;
   dXYZ(2,1) = a + b.*Y - d.*X.^2.*Y - c.*X.*Y;
   dXYZ(3,1) = e.*Z + b.^2.*Z - c.*Z.*X + d.*Y.*Z;
end

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