% lotka_volterra.m
%
% Imlements the Lotka-Volterra function
%   dx/dt = alpha x - beta xy
%   dy/dt = delta xy - gamma y
%
% Inputs:
%   t - Time variable: not used here because our equation
%       is independent of time, or 'autonomous'.
%   x - Independent variable: this contains both populations (x and y)
% Output:
%   dx - First derivative: the rate of change of the populations
function dx = lotka_volterra(t, x)
  dx = [0; 0];
  alpha = 1; 
  beta = .05; 
  delta = .02;
  gamma = .5;

  dx(1) = alpha * x(1) - beta * x(1) * x(2);
  dx(2) = delta * x(1) * x(2) - gamma * x(2);