You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: spm_dcm_delay.m
    path of file: ./repos/bspm/thirdparty/spm12
    
    the code of the file until where you have to start completion: function [Q,J] = spm_dcm_delay(P,M,J,N)
% returns the delay operator for flow and Jacobians of dynamical systems
% FORMAT [Q,J] = spm_dcm_delay(P,M)
% P   - model parameters
% M   - model specification structure
% J   - optional: system Jacobian

    
function [Q,J] = spm_dcm_delay(P,M,J,N)
% returns the delay operator for flow and Jacobians of dynamical systems
% FORMAT [Q,J] = spm_dcm_delay(P,M)
% P   - model parameters
% M   - model specification structure
% J   - optional: system Jacobian
% N   - optional: auto Taylor expansion [default: 2^6]
%
% Required fields:
%   M.f - dx/dt    = f(x,u,P,M)            {function string or m-file}
%   M.m - m inputs
%   M.n - n states
%   M.x - (n x 1) = x(0) = expansion point: defaults to x = 0;
%   M.u - (m x 1) = u    = expansion point: defaults to u = 0;
%
%
% Returns the delay operator for Jacobians of dynamical systems where the
% states are
%
% f     - dx(t)/dt  = f(x(t))
% Q     - delay operator dx(t)/dt = f(x(t - d))
%                                 = Q(d)*f(x(t))
% J     - Jacobian  = df/dt = (where delayed Jacobian = Q*J)
%
% If the delay martix is not specifed it is computed from its parameters in
% P.D (and M.pF.D if specified)
%__________________________________________________________________________
% Copyright (C) 2011 Wellcome Trust Centre for Neuroimaging

% Karl Friston
% $Id: spm_dcm_delay.m 7149 2017-08-08 13:14:36Z karl $

% order of Taylor approximation
%--------------------------------------------------------------------------
if nargin < 4, N = 2^8; end