MATLAB: Need help in solving diffrential equation with initial conditions. Kindly help me correct the code.

MATLABode

My objective is to solve for X_1 and X_2 with inital conditon x1(0) and x2(0) for time t=0 to 1000
syms x1(t) syms x2(t)
%constants
k1=0.015;k2=0.025;k3=0.038;
alpha=0;k=7;a=2;
%Initial Conditions
x1(0)=0.45+0.05*alpha;
x2(0)=0.65-0.15*alpha;
t=0:1000;
K_lower=k1+alpha(k2-k1);
K_upper=k3-alpha(k3-k2);
X_1=dsolve(diff(x1,t)==(K_lower)*(x1)*(1-(x2/k))*(x1-a),x1(0)==0.45+0.05*alpha);
X_2=dsolve(diff(x2,t)==(K_upper)*(x2)*(1-(x1/k))*(x2-a),x2(0)==0.65-0.15*alpha);
Error using sym/subsasgn (line 951)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be
symbolic variables, and function body must be sym expression.
Error in Initial_Conditions_alpha (line 4)
x1(0)=0.45+0.05*alpha;

Best Answer

You are defining the initial condition incorrectly. Check this code
syms x1(t) 
syms x2(t)
%constants
k1=0.015;k2=0.025;k3=0.038;
alpha=0;k=7;a=2;
K_lower=k1+alpha*(k2-k1);
K_upper=k3-alpha*(k3-k2);
Eq = [diff(x1,t)==(K_lower)*(x1)*(1-(x2/k))*(x1-a);
    diff(x2,t)==(K_upper)*(x2)*(1-(x1/k))*(x2-a)];
%Initial Conditions
conditions = [x1(0)==0.45+0.05*alpha;
    x2(0)==0.65-0.15*alpha];
X_1 = dsolve(Eq, conditions);
However, dsolve is used to find an analytical solution. It will return an empty vector because an analytical solution of your system does not exist. You need a numerical solver like ode45. Therefore, try this code next
k1=0.015;k2=0.025;k3=0.038;
alpha=0;k=7;a=2;
K_lower=k1+alpha*(k2-k1);
K_upper=k3-alpha*(k3-k2);
odefun = @(x) [(K_lower)*x(1)*(1-(x(2)/k))*(x(2)-a); ...
               (K_upper)*x(2)*(1-(x(1)/k))*(x(2)-a)];
tspan = [0 10];
conditions = [0.45+0.05*alpha; ...
              0.65-0.15*alpha];
          
[t, x] = ode45(@(t,x) odefun(x), tspan, conditions);
plot(t, y);
Related Question