Use MATLAB to solve the system. Consider the system (1) given by (x_1) = (-x_1 +

Question

Use MATLAB to solve the system.

Consider the system (1) given by (x_1) = (-x_1 + ax_2 + x_1^2 x_2) (x_2) = (b - ax_2 - x_1^2 x_2) Where x_1 represents the concentration of adenosine diphosphate and x_2 the concentration of fructose-6-phosphate, and a bare constants. It is a simple model of glycolysis Numerically solve system (1) using a = 0.06, b = 0.6, and x_1(0) = x_1* + epsilon, x_2(0) = x_2* + epsilon as initial conditions, where E is a small number and x* =(x_1*, x_2*)^T. Plot x_1(t) versus x_2(t) and the point x* = (x_1*, x_2*)^T, on the same figure. Also plot x_1(t) and x_2(t) as functions of time. *You will need to find the fixed point of the system.

Explanation / Answer

syms x1(t) x2(t)
a=0.6;
b=0.6;
ode1 = diff(x1) == -x1+a*x2+x1.^2*x2;
ode2 = diff(x2) == b-a*x2-x1.^2*x2;
odes = [ode1; ode2]
[x1Sol(t), x2Sol(t)] = dsolve(odes)
[x1Sub(t),x2Sub(t)]=subs([x1Sol(t), x2Sol(t)])

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