differential equations - Solving a system of ODEs with the Runge-Kutta method

I´m trying to solve a system of ODEs using a fourth-order Runge-Kutta method. I have to recreate certain results to obtain my degree. But I'm a beginner at Mathematica programming and with the Runge-Kutta method as well.

{A = 0.30, B = 1, C = 40, D = 1, E = 0.75, F = 0.11,
 r = 2.5, a = 2, e = 0.475, g = 2, d = 0.03, n = 0.01, p = -0.00005}

x'[t]/x[t] = (A + B x[t] - C x[t]^2 - F)/(D + E^(r y[t]));   
y'[t]/y[t] = g (((a s[t] x[t] k[t])/m[t]) - e) (1 - y[t]); 
m'[t]/m[t] = n;
k'[t]/k[t] = x[t] - d;
s'[t]/s[t] = -p;

I'd appreciate any kind of help. For over a month now, I've tried to solve this system myself but have only gotten bad results. This model is supposed to fluctuate around the equilibrium point, but in the code I have so far, this doesn't happen.

Answer

Here is a functional approach. The following will give you one step of the Runge-Kutta formula:

RungeKutta[func_List, yinit_List, y_List, step_] := 
 Module[{k1, k2, k3, k4},
  k1 = step N[func /. MapThread[Rule, {y, yinit}]];
  k2 = step N[func /. MapThread[Rule, {y, k1/2 + yinit}]];
  k3 = step N[func /. MapThread[Rule, {y, k2/2 + yinit}]];
  k4 = step N[func /. MapThread[Rule, {y, k3 + yinit}]];

  yinit + Total[{k1, 2 k2, 2 k3, k4}]/6]

Here, func is a list of functions, yinit a list of initial values, y a list of function variables (in your case that will be {x, y, m, k, s}, and step is the step size of the numerical simulation. You can then use something like NestList to iterate it many times like this:

NestList[RungeKutta[func, #, y, step] &, N[yinit], Round[t/step]]

Here, t is the maximum value of your independent variable. You can also include conditionals to check that the lists are of equal length.