In order to clamp the value of "x(:2)", you can reintialize the value over every iteration by assigning the new value within the funtion "f(t,x)". You would also require to set the derivative of "x(2)" to 0 as the value is clamped.
The following code helps you achieve the same in MATLAB R2023b:
tspan = 0:0.01:100;
x0(1) = 0.01;
x0(2) = 0.01*2; % To double the value of x0(2)
x0(3) = 0.01;
opts = odeset('AbsTol',1e-3);
% ODE Solver
[t,x] = ode23tb(@f, tspan, x0, opts);
% Adding a plot to visualize the changes
figure;
plot(t, x);
legend('x1', 'x2 (clamped)', 'x3');
xlabel('Time');
ylabel('Values');
title('ODE Solution with x2 Clamped');
function xdot = f(t, x)
xdot = zeros(3, 1);
c1 = 1; p1 = .57; p2 = .23; p3 = .995; p4 = 1;
% Clamping x(2) to its initial value
x(2) = 0.01*2;
R1 = x(1)*c1;
R2 = x(1) *c1*p1+x(2)*p2+p3;
R3 = 0.5;
R4 = x(2)*p4+x(3)*p3;
R5 = x(2)*c1+p3*x(3)+p4;
R6 = 0.05;
R7 = 0.005;
xdot(1) = (1/c1)*(( 1.0 * R1) + (-1.0 * R2) + (-1.0 * R3));
xdot(2) = 0; % Clamping x(2) by setting its derivative to zero
xdot(3) = (1/c1)*(( 1.0 * R6) + (-1.0 * R7));
end
Hope this helps!
