differential equations - Calculate ODE's with MATLAB -

the differential equations:

α'(t)=s(β-βα+α-qα^2)

β'(t)=(s^-1)(-β-αβ+γ)

γ'(t)=w(α-γ)

intitial values

α (0) = 30.00

β (0) = 1.000

γ (0) = 30.00

calculation

i want solve problem t_0=0 t=10 while using values s = 1, q = 1 , w = 0.1610

i've no idea how write function ode's , appreciate help!

i'm not in habit of solving other people's homework, today's lucky day guess.

so, have system of coupled ordinary differential equations:

α'(t) = s(β-α(β+1)-qα²)

β'(t) = (-β-αβ+γ)/s

γ'(t) = w(α-γ)

and want solve for

y = [α(t) β(t) γ(t)]

with 0 < t < 10, s = 1, q = 1, w = 0.1610. way in matlab define function computes derivative ([α'(t) β'(t) γ'(t)]), , throw in 1 of ode solvers (ode45 first bet):

s = 1; q = 1;  w = 0.1610;  % define y(t) = [α(t) β(t) γ(t)] = [y(1) y(2) y(3)]:  deriv = @(t,y) [...     s * (y(2) - y(1)*(y(2)+1) - q*y(1)^2)   % α'(t)     (-y(2) - y(1)*y(2) + y(3))/s            % β'(t)     w * (y(1)-y(3))                         % γ'(t) ];  % initial value y0 = [30 1 10];  % time span integrate on tspan = [0 10];  % solve ode numerically [t, y] = ode45(deriv, tspan, y0) 

this output

y =    30.0000    1.0000   10.0000    28.5635    0.9689   10.0049   % numerical solutions @ times t    27.2558    0.9413   10.0094    26.0603    0.9166   10.0136    ...        ...      ...    = α(t)     = β(t)   = γ(t)  t =          0     0.0016     0.0031   % corresponding times     0.0047     ... 

you can plot so:

figure, clf, hold on plot(t, y(:,1), 'r') plot(t, y(:,2), 'g') plot(t, y(:,3), 'b') legend('\alpha(t)', '\beta(t)', '\gamma(t)') 

which results in figure: