function dz=duffing(t,z) 

% Duffing's equations (general form):
%           
%   du/dt = v
%   dv/dt = -(omega_0)^2*u-beta*u^3-delta*v+gamma*cos(omega*t+phi)
%
% where u is the displacement, v is the velocity, 
% and the paramaters are constants.

dz=[z(2);(7.5*cos(t)-.05*z(2)-z(1)^3)]; 

 
% "Complex and Chaotic Nonlinear Dynamics. 
% Advances in Economics and Finance, 
% Mathematics and Statistics" 
% T.Vialar, Springer 2009
% Copyright(c).