Untitled

function dydt = bio_system(t, y)

    k1 = 0.5; 
    k2 = 1e-7;
    k3 = 0.6;

    B = y(1);
    S = y(2);

    dBdt = (k1 * B * S) / (k2 + S);
    dSdt = -k3*(k1*B*S) / (k2 + S);

    dydt = [dBdt; dSdt];
end

B0 = 0.03;
S0 = 4.5;
y0 = [B0; S0];

tspan = [0 15];

options = odeset('RelTol', 1e-8, 'AbsTol', 1e-12);

[t, y] = ode45(@bio_system, tspan, y0, options);

figure(1)
plot(t, y(:, 1), 'b-', 'LineWidth', 1.5)
grid on
xlabel('Tempo (h)')
ylabel('Biomassa')
title('Evoluzione della biomassa')

figure(2)
plot(t, y(:,2), 'r-', 'LineWidth', 1.5)
grid on
xlabel('Tempo (h)')
ylabel('Substrato')
title('Evoluzione del substrato')

fprintf('Valori finali dopo 15 ore:\n')
fprintf('Biomassa: %.4f kmol/m^3\n', y(end,1))
fprintf('Substrato: %.4f kmol/m^3\n', y(end,2))